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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

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 October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)