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 A001708 Generalized Stirling numbers. (Formerly M5095 N2206) 2
 1, 20, 295, 4025, 54649, 761166, 11028590, 167310220, 2664929476, 44601786944, 784146622896, 14469012689040, 279870212258064, 5667093514231200, 119958395537083104, 2650594302549806976, 61049697873641191296, 1463708634867162093312, 36482312832434713195776 (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=2) ~ exp(-x)/x^5*(1 - 20/x + 295/x^2 - 4025/x^3 + 54649/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 E.g.f.: ( log ( 1 - x ))^4 / 24 ( 1 - x )^2. a(n)=sum((-1)^(n+k)*binomial(k+4, 4)*2^k*stirling1(n+4, k+4), 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-4) = |f(n,4,2)|, for n>=4. [From Milan Janjic, Dec 21 2008] MATHEMATICA With[{nn=20}, Drop[CoefficientList[Series[Log[1-x]^4/(24(1-x)^2), {x, 0, nn}], x]Range[0, nn]!, 4]] (* Harvey P. Dale, Oct 24 2011 *) CROSSREFS Sequence in context: A223956 A132168 A069326 * A016255 A322052 A250014 Adjacent sequences:  A001705 A001706 A001707 * A001709 A001710 A001711 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.)