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A001718 Generalized Stirling numbers.
(Formerly M5127 N2222)
2
1, 22, 355, 5265, 77224, 1155420, 17893196, 288843260, 4876196776, 86194186584, 1595481972864, 30908820004608, 626110382381184, 13246845128678016, 292374329134060800, 6723367631258860800, 160883166944083161600, 4001062259532015244800 (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=4) ~ exp(-x)/x^4*(1 - 22/x + 355/x^2 - 5265/x^3 + 77224/x^4 - 1155420/x^5 + ... ) leads to the sequence given above. See A163931 and A163934 for more information. - 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 relies aux nombres de Stirling, Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. 77 (1962).

FORMULA

a(n) = sum((-1)^(n+k)*binomial(k+3, 3)*4^k*stirling1(n+3, k+3), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

E.g.f.: (1-15*log(1-x)+37*log(1-x)^2-20*log(1-x)^3)/(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-3) = |f(n,3,4)|, for n>=3. - Milan Janjic, Dec 21 2008

MATHEMATICA

nn = 20; t = Range[0, nn]! CoefficientList[Series[(1 - 15*Log[1 - x] + 37*Log[1 - x]^2 - 20*Log[1 - x]^3)/(1 - x)^7, {x, 0, nn}], x] (* T. D. Noe, Aug 09 2012 *)

PROG

(PARI) a(n) = sum(k=0, n, (-1)^(n+k)*binomial(k+3, 3)*4^k*stirling(n+3, k+3, 1)); \\ Michel Marcus, Jan 20 2016

CROSSREFS

Sequence in context: A016265 A208458 A016263 * A199671 A253878 A081127

Adjacent sequences:  A001715 A001716 A001717 * A001719 A001720 A001721

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 15 18:14 EST 2019. Contains 319153 sequences. (Running on oeis4.)