A051565 Third unsigned column of triangle A051523.

0, 0, 1, 33, 791, 17100, 358024, 7491484, 159168428, 3463513704, 77559615576, 1792139785920, 42789106278720, 1056302350122240, 26964471256888320, 711643650545422080, 19410244660543737600, 546854985563699289600

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=10) ~ exp(-x)/x^3*(1 - 33/x + 791/x^2 - 17100/x^3 + 358024/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 A051523.

Links

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

Formula

a(n) = A051523(n, 2)*(-1)^n; e.g.f.: ((log(1-x))^2)/(2*(1-x)^10).

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,2,10)|, for n>=1. - Milan Janjic, Dec 21 2008

Crossrefs

Cf. A049398 (m=0), A051564 (m=1) unsigned columns.

Sequence in context: A021021 A164750 A100788 * A014931 A197358 A299074

Adjacent sequences: A051562 A051563 A051564 * A051566 A051567 A051568

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved