A051563 Third unsigned column of triangle A051380.

0, 0, 1, 30, 659, 13145, 255424, 4985316, 99236556, 2030997852, 42924478536, 938984014584, 21283428847680, 500043968498880, 12176238355176960, 307176581692097280, 8023946251816984320, 216880826334455750400

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=9) ~ exp(-x)/x^3*(1 - 30/x + 659/x^2 - 13145/x^3 + 255424/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 A051380.

Crossrefs

Cf. A049389 (m=0), A051562 (m=1) unsigned columns.

Formula

a(n) = A051380(n, 2)*(-1)^n; e.g.f.: ((log(1-x))^2)/(2*(1-x)^9).

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,2,9)|, for n>=1. - Milan Janjic, Dec 21 2008