A051546 Third unsigned column of triangle A051339.

0, 0, 1, 24, 431, 7155, 117454, 1961470, 33775244, 603682596, 11235811536, 218055250512, 4413843664416, 93156324734304, 2048591287486080, 46898664421553280, 1116592842912341760, 27618683992928743680

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=7) ~ exp(-x)/x^3*(1 - 24/x + 431/x^2 - 7155/x^3 + 117454/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 A051339.

Crossrefs

Cf. A001730 (m=0), A051545 (m=1) unsigned columns.

Formula

a(n) = A051339(n, 2)*(-1)^n; e.g.f.: (log(1-x))^2/(2*(1-x)^7).

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,2,7)|, for n>=1. - Milan Janjic, Dec 21 2008