A051525 Third unsigned column of triangle A051338.

0, 0, 1, 21, 335, 5000, 74524, 1139292, 18083484, 299705400, 5198985576, 94461323616, 1797180658272, 35776357096896, 744402741205824, 16169795109262080, 366214212167489280, 8636605663418933760

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=6) ~ exp(-x)/x^3*(1 - 21/x + 335/x^2 - 5000/x^3 + 74524/x^4 - 1139292/x^5 + ...) 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 A051338.

Crossrefs

Cf. A001725 (m=0), A051524 (m=1) unsigned columns.

Formula

a(n) = A051338(n, 2)*(-1)^n; e.g.f.: (log(1-x))^2/(2*(1-x)^6).

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,2,6)|, for n>=1. - Milan Janjic, Dec 21 2008