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 A001722 Generalized Stirling numbers. (Formerly M5061 N2191) 2
 1, 18, 251, 3325, 44524, 617624, 8969148, 136954044, 2201931576, 37272482280, 663644774880, 12413008539360, 243533741849280, 5003753991174720, 107497490419296000, 2410964056571616000, 56366432074677312000, 1371711629236971456000, 34699437370290760704000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The asymptotic expansion of the higher order exponential integral E(x,m=3,n=5) ~ exp(-x)/x^3*(1 - 18/x + 251/x^2 - 3325/x^3 + 44524/x^4 - 617624/x^5 + ... ) leads to the sequence given above. See A163931 and A163932 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 FORMULA a(n)=sum((-1)^(n+k)*binomial(k+2, 2)*5^k*stirling1(n+2, k+2), 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-2) = |f(n,2,5)|, for n>=2. [From Milan Janjic, Dec 21 2008] MATHEMATICA Table[Sum[(-1)^(n + k)*Binomial[k + 2, 2]*5^k*StirlingS1[n + 2, k + 2], {k, 0, n}], {n, 0, 20}] (* T. D. Noe, Aug 10 2012 *) CROSSREFS Sequence in context: A154241 A154250 A154350 * A060788 A144708 A020528 Adjacent sequences:  A001719 A001720 A001721 * A001723 A001724 A001725 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 January 19 20:33 EST 2019. Contains 319310 sequences. (Running on oeis4.)