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 A001709 Generalized Stirling numbers. (Formerly M5195 N2259) 3
 1, 27, 511, 8624, 140889, 2310945, 38759930, 671189310, 12061579816, 225525484184, 4392554369840, 89142436976320, 1884434077831824, 41471340993035856, 949385215397800224, 22587683825903611680, 557978742043520648256, 14297219701868137003200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The asymptotic expansion of the higher order exponential integral E(x,m=6,n=2) ~ exp(-x)/x^6*(1 - 27/x + 511/x^2 - 8624/x^3 + 140889/x^4 - ...) leads to the sequence given above. See A163931 for E(x,m,n) information and A163932 for a Maple procedure for the asymptotic expansion. - Johannes W. Meijer, Oct 20 2009 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). LINKS T. D. Noe, Table of n, a(n) for n = 0..100 Robert E. Moritz, On the sum of products of n consecutive integers, Univ. Washington Publications in Math., 1 (No. 3, 1926), 44-49 [Annotated scanned copy] FORMULA a(n)=sum((-1)^(n+k)*binomial(k+5, 5)*2^k*stirling1(n+5, k+5), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004 E.g.f.: (6-120*log(1-x)+465*log(1-x)^2-580*log(1-x)^3+261*log(1-x)^4-36*log(1-x)^5)/(6*(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-5) = |f(n,5,2)|, for n>=5. [From Milan Janjic, Dec 21 2008] MATHEMATICA nn = 25; t = Range[0, nn]! CoefficientList[Series[-Log[1 - x]^5/(120*(1 - x)^2), {x, 0, nn}], x]; Drop[t, 5] (* T. D. Noe, Aug 09 2012 *) CROSSREFS Sequence in context: A020568 A021734 A019752 * A016887 A110896 A215039 Adjacent sequences:  A001706 A001707 A001708 * A001710 A001711 A001712 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 18 15:21 EDT 2019. Contains 328162 sequences. (Running on oeis4.)