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

0,4

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.

Links

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

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

Crossrefs

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

Sequence in context: A264849 A111779 A075473 * A152499 A027475 A180801

Adjacent sequences: A051560 A051561 A051562 * A051564 A051565 A051566

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved