A326996 Main diagonal of A260876.

1, 1, 4, 365, 3086331, 5612271711927, 3829797188212731601783, 1478967550753025951356611840021161, 452501475882033837823819972299248189399008553836, 146630849220097180917463638217405949960396188742877031073909770851

Offset: 0

Author

Peter Luschny, Aug 13 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..27

Crossrefs

Cf. A260876, A327001.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(
       binomial(k*n-1, k*j-1)*b(n-j, k), j=1..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..10);  # Alois P. Heinz, Aug 14 2019

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Binomial[k n - 1, k j - 1] b[n - j, k], {j, 1, n}]];
a[n_] := b[n, n];
a /@ Range[0, 10] (* Jean-François Alcover, Nov 07 2020, after Maple *)

Formula

a(n) = A260876(n,n).

a(n) = (n^2)! * [x^(n^2)] exp(Sum_{k>=1} x^(n*k) / (n*k)!). - Ilya Gutkovskiy, Feb 09 2020