A343584 a(n) = Sum_{j=0..n}(-1)^(n-j)*binomial(n, j)*A028246(n+1, j+1).

1, 0, -3, -10, 25, 574, 2653, -30234, -644079, -2438722, 102934381, 2094370486, 680814121, -762930678498, -14273311787139, 102712339811654, 10395244787594401, 165359347094406526, -3771699711640161587, -231946002714537442026, -2649765469158480160839

Offset: 0

Author

Peter Luschny, Apr 28 2021

Keywords

• sign

Crossrefs

Cf. A028246, A173018.

Programs

Maple

T := (n, k) -> add(combinat:-eulerian1(n, j)*binomial(n-j, n-k), j=0..n):
a := n -> add((-1)^(n-j)*T(n, j)*binomial(n, j), j=0..n): seq(a(n), n=0..22);

PARI

T(n, j) = stirling(n, k, 2)*(k-1)!; \\ A028246
a(n) = sum(j=0, n, (-1)^(n-j)*binomial(n, j)*T(n+1, j+1)); \\ Michel Marcus, May 04 2021