A308327 a(n) = (1/n!) * Sum_{i_1=1..n} Sum_{i_2=1..n} ... Sum_{i_n=1..n} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).

1, -1, 1, -120, 1056496, -2063348839223, 1457689055077930674637, -569779896381467292745562607320194, 174622933743914766946635359968704455433117668396, -56466564044341292662007179162722871704054012257606338926938133618

Offset: 0

Author

Seiichi Manyama, May 20 2019

Keywords

• sign

Examples

			a(2) = (1/2) * (binomial(1+1,1) - binomial(1+2,2) - binomial(2+1,1) + binomial(2+2,2)) = 1.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..27

Crossrefs

Main diagonal of A308356.

Cf. A308296.

Programs

PARI

{a(n) = sum(i=n, n^2, (-1)^i*i!*polcoef(sum(j=1, n, x^j/j!)^n, i))/n!}