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Search: id:A001706
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| A001706 |
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Generalized Stirling numbers.
(Formerly M4646 N1988)
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+0
5
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| 1, 9, 71, 580, 5104, 48860, 509004, 5753736, 70290936, 924118272, 13020978816, 195869441664, 3134328981120, 53180752331520, 953884282141440, 18037635241029120, 358689683932346880, 7483713725055744000
(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=3,n=2) ~ exp(-x)/x^3*(1 - 9/x + 71/x^2 - 580/x^3 + 5104/x^4 - 48860/x^5+ the sequence given above. See A163931 and A163932 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 )^2 / 2 ( 1 - x )^2.
a(n)=sum((-1)^(n+k)*binomial(k+2, 2)*2^k*stirling1(n+2, k+2), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
a(n-1)=(1/2)*sum(i=0, n, C(n, i)*A000254(i)*A000254(n-i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2004
If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n-1) = |f(n,2,2)|, for n>=2. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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CROSSREFS
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Sequence in context: A081900 A164551 A057080 this_sequence A158193 A123987 A003365
Adjacent sequences: A001703 A001704 A001705 this_sequence A001707 A001708 A001709
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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 Christian G. Bower (bowerc(AT)usa.net).
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