A351779 a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * (n-k)^k/k!.

1, -1, 4, -63, 2288, -138525, 12381084, -1528482823, 249005711296, -51739455340953, 13353206066063900, -4190486732316600771, 1571373340568392914288, -693899460077821703051125, 356404409990391961980227068, -210670220153918100996704166975

Offset: 0

Author

Seiichi Manyama, Feb 19 2022

Keywords

• sign

Crossrefs

Main diagonal of A351776.

Cf. A351765, A351780.

Programs

PARI

a(n) = n!*sum(k=0, n, (-n)^(n-k)*(n-k)^k/k!);

Formula

a(n) = n! * [x^n] 1/(1 + n*x*exp(x)).