A344052 - OEIS

A344052

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*E1(n, k).

1, -1, -1, 8, 19, -276, -1002, 21216, 103395, -2881180, -17620142, 609297072, 4483215086, -185182296040, -1592692090420, 76512069014400, 753146574607395, -41256108712556460, -457383584443526790, 28138583115102810000, 346933879489006727610, -23683708768534714984920

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OFFSET

0,4

COMMENTS

Inverse binomial convolution of the first order Eulerian numbers (A173018).

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(n - k - j)*(j - k - 1)^n * binomial(n, k)* binomial(n+1, j).

MAPLE

A344052 := n -> add((-1)^(n-k)*binomial(n, k)*combinat:-eulerian1(n, k), k=0..n):

seq(A344052(n), n=0..21);