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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

N. J. A. Sloane

EXTENSIONS

More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

STATUS

approved

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Last modified January 20 04:43 EST 2019. Contains 319323 sequences. (Running on oeis4.)