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 A001707 Generalized Stirling numbers. (Formerly M4947 N2119) 3
 1, 14, 155, 1665, 18424, 214676, 2655764, 34967140, 489896616, 7292774280, 115119818736, 1922666722704, 33896996544384, 629429693586048, 12283618766690304, 251426391808144896, 5387217520095244800, 120615281647055884800, 2817014230489985049600 (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=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. - 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 E.g.f.: - log ( 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 Janjic, Dec 21 2008] MATHEMATICA nn = 23; t = Range[0, nn]! CoefficientList[Series[-Log[1 - x]^3/(6*(1 - x)^2), {x, 0, nn}], x]; Drop[t, 3] (* T. D. Noe, Aug 09 2012 *) CROSSREFS Sequence in context: A006865 A263474 A154347 * A078999 A016157 A238770 Adjacent sequences:  A001704 A001705 A001706 * A001708 A001709 A001710 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 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)