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Search: id:A001711
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| A001711 |
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Generalized Stirling numbers.
(Formerly M4429 N1873)
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+0
8
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| 1, 7, 47, 342, 2754, 24552, 241128, 2592720, 30334320, 383970240, 5231113920, 76349105280, 1188825724800, 19675048780800, 344937224217600, 6386713749964800, 124548748102195200, 2551797512248320000
(list; graph; listen)
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OFFSET
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0,2
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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=2,n=3) ~ exp(-x)/x^2*(1 - 7/x + 47/x^2 - 342/x^3 + 2754/x^4 - 24552/x^5 + 241128/x^6 - ... ) leads to the sequence given above. See A163931 and A028421 for more information.
(End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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FORMULA
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E.g.f.: - ln ( 1 - x ) / ( 1 - x )^3.
a(n)=sum((-1)^(n+k)*(k+1)*3^k*stirling1(n+1, k+1), k=0..n); - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
a(n)=n!*sum((-1)^k*binomial(-3,k)/(n-k),k=0..n-1); [From Milan R. Janjic (agnus(AT)blic.net), Dec 14 2008]
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MAPLE
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a:=n->sum(1/2*(n!/k), k=3..n): seq(a(n), n=3..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 22 2008
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CROSSREFS
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Sequence in context: A098405 A104092 A024187 this_sequence A088057 A108434 A093173
Adjacent sequences: A001708 A001709 A001710 this_sequence A001712 A001713 A001714
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
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