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A326996 Main diagonal of A260876.

%I A326996 #12 Nov 07 2020 16:28:23
%S A326996 1,1,4,365,3086331,5612271711927,3829797188212731601783,
%T A326996 1478967550753025951356611840021161,
%U A326996 452501475882033837823819972299248189399008553836,146630849220097180917463638217405949960396188742877031073909770851
%N A326996 Main diagonal of A260876.
%H A326996 Alois P. Heinz, <a href="/A326996/b326996.txt">Table of n, a(n) for n = 0..27</a>
%F A326996 a(n) = A260876(n,n).
%F A326996 a(n) = (n^2)! * [x^(n^2)] exp(Sum_{k>=1} x^(n*k) / (n*k)!). - _Ilya Gutkovskiy_, Feb 09 2020
%p A326996 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A326996        binomial(k*n-1, k*j-1)*b(n-j, k), j=1..n))
%p A326996     end:
%p A326996 a:= n-> b(n$2):
%p A326996 seq(a(n), n=0..10);  # _Alois P. Heinz_, Aug 14 2019
%t A326996 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 A326996 a[n_] := b[n, n];
%t A326996 a /@ Range[0, 10] (* _Jean-François Alcover_, Nov 07 2020, after Maple *)
%Y A326996 Cf. A260876, A327001.
%K A326996 nonn
%O A326996 0,3
%A A326996 _Peter Luschny_, Aug 13 2019