A336172 a(n) = Sum_{k=0..n} (-1)^(n-k) * multinomial(n+(n-1)*k; n-k, {k}^n).

1, 0, 1, 1109, 58370761, 616967236620839, 2667424979594724623421841, 7363013376580445620328429354795257679, 18165626590057176919253932602358956717053291818375681, 53130672834302729155813211757017136527240145191602729876485547920535679

Offset: 0

Author

Seiichi Manyama, Jul 10 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Main diagonal of A336169.

Cf. A229267.

Programs

Mathematica

a[n_] := Sum[(-1)^(n - k)*(n + (n - 1)*k)!/((n - k)!*k!^n), {k, 0, n}]; Array[a, 10, 0] (* Amiram Eldar, Jul 10 2020 *)

PARI

{a(n) = sum(k=0, n, (-1)^(n-k)*(n+(n-1)*k)!/((n-k)!*k!^n))}

Formula

a(n) = [x^n] Sum_{k=0..n} (n*k)!/k!^n * x^k / (1+x)^(n*k+1).