A051561 Third unsigned column of triangle A051379.

0, 0, 1, 27, 539, 9850, 176554, 3197348, 59354028, 1137868848, 22614500016, 466814750688, 10015620672672, 223359393479040, 5175622796192640, 124533006364442880, 3109120944743427840, 80473740053567016960

Offset

0,4

Comments

From Johannes W. Meijer, Oct 20 2009: (Start)

The asymptotic expansion of the higher order exponential integral E(x,m=3,n=8) ~ exp(-x)/x^3*(1 - 27/x + 539/x^2 - 9850/x^3 + 176554/x^4 + ...) leads to the sequence given above. See A163931 and A163932 for more information.

(End)

References

Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051379.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = A051379(n, 2)*(-1)^n; e.g.f.: ((log(1-x))^2)/(2*(1-x)^8).

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) = |f(n,2,8)|, for n>=1. - Milan Janjic, Dec 21 2008

Mathematica

With[{nn=20}, CoefficientList[Series[(Log[1-x])^2/(2(1-x)^8), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 10 2013 *)

Crossrefs

Cf. A049388 (m=0), A051560 (m=1) unsigned columns.

Sequence in context: A215039 A014928 A163199 * A163197 A347591 A267544

Adjacent sequences: A051558 A051559 A051560 * A051562 A051563 A051564

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved