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A001712
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Generalized Stirling numbers.
(Formerly M4861 N2077)
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1
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1, 12, 119, 1175, 12154, 133938, 1580508, 19978308, 270074016, 3894932448, 59760168192, 972751628160, 16752851775360, 304473528961920, 5825460745532160, 117070467915075840, 2465958106403712000
(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=3,n=3) ~ exp(-x)/x^3*(1 - 12/x + 119/x^2 - 1175/x^3 + 12154/x^4 - 133938/x^5 + ... ) leads to the sequence given above. See A163931 and A163932 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
| a(n)=sum((-1)^(n+k)*binomial(k+2, 2)*3^k*stirling1(n+2, k+2), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
E.g.f.: (1-7*ln(1-x)+6*ln(1-x)^2)/(1-x)^5. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 01 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-2) = |f(n,2,3)|, for n>=2. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]
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CROSSREFS
| Sequence in context: A180777 A163950 A025132 * A077251 A075622 A153054
Adjacent sequences: A001709 A001710 A001711 * A001713 A001714 A001715
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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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