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A001707
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Generalized Stirling numbers.
(Formerly M4947 N2119)
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2
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1, 14, 155, 1665, 18424, 214676, 2655764, 34967140, 489896616, 7292774280, 115119818736, 1922666722704, 33896996544384, 629429693586048, 12283618766690304, 251426391808144896, 5387217520095244800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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=4,n=2) ~ exp(-x)/x^4*(1 - 14/x + 155/x^2 - 1665/x^3 + 18424/x^4 - 214676/x^5 + ...) leads to the sequence given above. See A163931 and A163934 for more information.
(End)
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REFERENCES
| 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
| E.g.f.: - ln ( 1 - x )^3 / 6 ( x - 1 )^2.
a(n)=sum((-1)^(n+k)*binomial(k+3, 3)*2^k*stirling1(n+3, k+3), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 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-3) = |f(n,3,2)|, for n>=3. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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CROSSREFS
| Sequence in context: A154248 A006865 A154347 * A078999 A016157 A199703
Adjacent sequences: A001704 A001705 A001706 * A001708 A001709 A001710
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
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