A326996 - OEIS

%I #12 Nov 07 2020 16:28:23

%S 1,1,4,365,3086331,5612271711927,3829797188212731601783,

%T 1478967550753025951356611840021161,

%U 452501475882033837823819972299248189399008553836,146630849220097180917463638217405949960396188742877031073909770851

%N Main diagonal of A260876.

%H Alois P. Heinz, <a href="/A326996/b326996.txt">Table of n, a(n) for n = 0..27</a>

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

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

%p b:= proc(n, k) option remember; `if`(n=0, 1, add(

%p        binomial(k*n-1, k*j-1)*b(n-j, k), j=1..n))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..10);  # _Alois P. Heinz_, Aug 14 2019

%t 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}]];

%t a[n_] := b[n, n];

%t a /@ Range[0, 10] (* _Jean-François Alcover_, Nov 07 2020, after Maple *)

%Y Cf. A260876, A327001.

%K nonn

%O 0,3

%A _Peter Luschny_, Aug 13 2019