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Search: id:A001716
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| A001716 |
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Generalized Stirling numbers.
(Formerly M4651 N1990)
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+0
7
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| 1, 9, 74, 638, 5944, 60216, 662640, 7893840, 101378880, 1397759040, 20606463360, 323626665600, 5395972377600, 95218662067200, 1773217155225600, 34758188233574400, 715437948072960000, 15429680577561600000
(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=4) ~ exp(-x)/x^2*(1 - 9/x + 74/x^2 - 638/x^3 + 5944/x^4 - 60216/x^5 + 662640/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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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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FORMULA
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a(n) = sum((-1)^(n+k)*(k+1)*4^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(-4,k)/(n-k),k=0..n-1); [From Milan R. Janjic (agnus(AT)blic.net), Dec 14 2008]
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CROSSREFS
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Sequence in context: A075232 A145524 A037533 this_sequence A028991 A102094 A125397
Adjacent sequences: A001713 A001714 A001715 this_sequence A001717 A001718 A001719
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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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