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Search: id:A001720
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| A001720 |
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n!/24.
(Formerly M3960 N1634)
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+0
33
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| 1, 5, 30, 210, 1680, 15120, 151200, 1663200, 19958400, 259459200, 3632428800, 54486432000, 871782912000, 14820309504000, 266765571072000, 5068545850368000, 101370917007360000, 2128789257154560000
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 20 2009: (Start)
The asymptotic expansion of the higher order exponential integral E(x,m=1,n=5) ~ exp(-x)/x*(1 - 5/x + 30/x^2 - 210/x^3 + 1680/x^4 - 15120/x^5 + 151200/x^6 - 1663200/x^7 + ... ) leads to the sequence given above. See A163931 and A130534 for more information.
(End)
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REFERENCES
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Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 264
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
Index entries for sequences related to factorial numbers
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FORMULA
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E.g.f. if offset 0: 1/(1-x)^5.
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MAPLE
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a[0]:=1:a[1]:=1:for n from 2 to 50 do a[n]:=(a[n-1]*(n+2)^2) od: seq(sqrt(a[n])/4, n=2..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 04 2008
a:=n->mul(denom((k+1)/(k+2) ), k=3..n): seq(a(n), n=2..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008
a:=n->mul(numer((k+1)/(k+2) ), k=4..n): seq(a(n), n=3..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008
a:=n->mul((j-1), j=6..n):seq(a(n), n=5..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2008]
restart: G(x):=1/(1-x)^5: f[0]:=G(x): for n from 1 to 18 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..17); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]
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MATHEMATICA
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a[n_]:=n!/24; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 13 2008]
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PROGRAM
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(Other) sage: [binomial(n, 4)*factorial (n-4) for n in xrange(4, 22)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
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CROSSREFS
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Cf. A049459, A051338. a(n)= A049353(n-3, 1) (first column of triangle).
Sequence in context: A144180 A091122 A029587 this_sequence A051829 A058247 A137965
Adjacent sequences: A001717 A001718 A001719 this_sequence A001721 A001722 A001723
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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