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 A001718 Generalized Stirling numbers. (Formerly M5127 N2222) 3
 1, 22, 355, 5265, 77224, 1155420, 17893196, 288843260, 4876196776, 86194186584, 1595481972864, 30908820004608, 626110382381184, 13246845128678016, 292374329134060800, 6723367631258860800, 160883166944083161600, 4001062259532015244800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The asymptotic expansion of the higher order exponential integral E(x,m=4,n=4) ~ exp(-x)/x^4*(1 - 22/x + 355/x^2 - 5265/x^3 + 77224/x^4 - 1155420/x^5 + ... ) leads to the sequence given above. See A163931 and A163934 for more information. - Johannes W. Meijer, Oct 20 2009 REFERENCES 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). LINKS T. D. Noe, Table of n, a(n) for n = 0..100 D. S. Mitrinovic, M. S. Mitrinovic, Tableaux d'une classe de nombres relies aux nombres de Stirling, Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. 77 (1962). FORMULA a(n) = sum((-1)^(n+k)*binomial(k+3, 3)*4^k*stirling1(n+3, k+3), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004 E.g.f.: (1-15*log(1-x)+37*log(1-x)^2-20*log(1-x)^3)/(1-x)^7. - Vladeta Jovovic, 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-3) = |f(n,3,4)|, for n>=3. - Milan Janjic, Dec 21 2008 MATHEMATICA nn = 20; t = Range[0, nn]! CoefficientList[Series[(1 - 15*Log[1 - x] + 37*Log[1 - x]^2 - 20*Log[1 - x]^3)/(1 - x)^7, {x, 0, nn}], x] (* T. D. Noe, Aug 09 2012 *) PROG (PARI) a(n) = sum(k=0, n, (-1)^(n+k)*binomial(k+3, 3)*4^k*stirling(n+3, k+3, 1)); \\ Michel Marcus, Jan 20 2016 CROSSREFS Sequence in context: A016265 A208458 A016263 * A199671 A253878 A081127 Adjacent sequences:  A001715 A001716 A001717 * A001719 A001720 A001721 KEYWORD nonn AUTHOR EXTENSIONS More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004 STATUS approved

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Last modified October 17 16:20 EDT 2019. Contains 328117 sequences. (Running on oeis4.)