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 A001719 Generalized Stirling numbers. (Formerly M5212 N2266) 5
 1, 30, 625, 11515, 203889, 3602088, 64720340, 1194928020, 22800117076, 450996059800, 9262414989464, 197632289814960, 4381123888865424, 100869322905986496, 2410630110159777216, 59757230054773959552, 1535299458203884231296, 40848249256425236795904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The asymptotic expansion of the higher order exponential integral E(x,m=5,n=4) ~ exp(-x)/x^5*(1 - 30/x + 625/x^2 - 11515/x^3 + 203889/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 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 reliés aux nombres de Stirling, Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. 77 (1962). FORMULA E.g.f.: (log(1-x)/(1-x))^4/24. - Vladeta Jovovic, May 05 2003 a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(k+4, 4)*4^k*Stirling1(n+4, k+4). - 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-4) = |f(n,4,4)|, for n>=4. - Milan Janjic, Dec 21 2008 MATHEMATICA nn = 24; t = Range[0, nn]! CoefficientList[Series[(Log[1 - x]/(1 - x))^4/24, {x, 0, nn}], x]; Drop[t, 4] (* T. D. Noe, Aug 09 2012 *) PROG (PARI) a(n) = sum(k=0, n, (-1)^(n+k)*binomial(k+4, 4)*4^k*stirling(n+4, k+4, 1)); \\ Michel Marcus, Jan 20 2016 CROSSREFS Cf. A000254, A001706, A001713. Sequence in context: A028258 A285235 A075911 * A004359 A001777 A205828 Adjacent sequences: A001716 A001717 A001718 * A001720 A001721 A001722 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, May 05 2003 STATUS approved

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Last modified March 28 05:31 EDT 2023. Contains 361577 sequences. (Running on oeis4.)