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

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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.

Crossrefs

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

Programs

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 *)

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