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A001714 Generalized Stirling numbers.
(Formerly M5184 N2252)
3
1, 25, 445, 7140, 111769, 1767087, 28699460, 483004280, 8460980836, 154594537812, 2948470152264, 58696064973000, 1219007251826064, 26390216795274288, 594982297852020288, 13955257961738192448, 340154857108405040256, 8606960634143667938688 (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=3) ~ exp(-x)/x^5*(1 - 25/x + 445/x^2 - 7140/x^3 + 111769/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

FORMULA

a(n)=sum((-1)^(n+k)*binomial(k+4, 4)*3^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,4,3)|, for n>=4. [From Milan Janjic, Dec 21 2008]

MATHEMATICA

nn = 24; t = Range[0, nn]! CoefficientList[Series[Log[1 - x]^4/(24*(1 - x)^3), {x, 0, nn}], x]; Drop[t, 4] (* T. D. Noe, Aug 09 2012 *)

CROSSREFS

Sequence in context: A018207 A264382 A260854 * A016633 A001811 A131279

Adjacent sequences:  A001711 A001712 A001713 * A001715 A001716 A001717

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 18 07:18 EST 2019. Contains 319269 sequences. (Running on oeis4.)