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A358145 a(n) = Sum_{k=0..n} binomial(n*k,k) * binomial(n*(n-k),n-k).

%I A358145 #13 Nov 01 2022 10:36:43
%S A358145 1,2,16,258,6184,195660,7674144,358788696,19464910000,1201543131276,
%T A358145 83134800597280,6371436086078382,535715287899894216,
%U A358145 49025879014213908144,4850781409411286177248,515964243167132532702480,58710263012322890445554400
%N A358145 a(n) = Sum_{k=0..n} binomial(n*k,k) * binomial(n*(n-k),n-k).
%H A358145 Seiichi Manyama, <a href="/A358145/b358145.txt">Table of n, a(n) for n = 0..337</a>
%F A358145 a(n) = Sum_{k=0..n} (n-1)^(n-k) * binomial(n^2+1,k).
%F A358145 a(n) = Sum_{k=0..n} n^(n-k) * binomial((n-1)*n+k,k).
%F A358145 a(n) ~ exp(n - 1/2) * n^n / 2. - _Vaclav Kotesovec_, Nov 01 2022
%o A358145 (PARI) a(n) = sum(k=0, n, binomial(n*k, k)*binomial(n*(n-k), n-k));
%o A358145 (PARI) a(n) = sum(k=0, n, (n-1)^(n-k)*binomial(n^2+1, k));
%o A358145 (PARI) a(n) = sum(k=0, n, n^(n-k)*binomial((n-1)*n+k, k));
%Y A358145 Main diagonal of A358050.
%K A358145 nonn
%O A358145 0,2
%A A358145 _Seiichi Manyama_, Oct 31 2022