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A303921 Main diagonal of triangle A303920: a(n) = A303920(n,n) for n>=0.

%I A303921 #14 Oct 08 2019 10:40:56
%S A303921 1,1,6,56,722,12012,246092,6002824,170048394,5489377628,198966923232,
%T A303921 8002061191632,353657146741108,17038311744899928,888756685396257456,
%U A303921 49903123853737160256,3001090647251938886634,192456294604677056842812,13110208254597852188752232,945417747582856587884200944,71952514694665595216762956518,5763451519600988678663191769380
%N A303921 Main diagonal of triangle A303920: a(n) = A303920(n,n) for n>=0.
%C A303921 G.f. of A303920: (1-y) * Sum_{n>=0} y^n * (1 + x*(1-y)^2)^(n^2)  =  Sum_{n>=0} Sum_{k=0..2*n} A303920(n,k)*x^n*y^k; this sequence is A303920(n,n) for n>=0.
%H A303921 Paul D. Hanna, <a href="/A303921/b303921.txt">Table of n, a(n) for n = 0..50</a>
%F A303921 a(n) ~ sqrt(3) * 2^(2*n + 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). - _Vaclav Kotesovec_, Oct 08 2019
%e A303921 Triangle A303920 begins:
%e A303921 [1];
%e A303921 [0, 1, 1];
%e A303921 [0, 0, 6, 6, 0];
%e A303921 [0, 0, 4, 56, 56, 4, 0];
%e A303921 [0, 0, 1, 117, 722, 722, 117, 1, 0];
%e A303921 [0, 0, 0, 126, 2982, 12012, 12012, 2982, 126, 0, 0];
%e A303921 [0, 0, 0, 84, 6916, 79548, 246092, 246092, 79548, 6916, 84, 0, 0]; ...
%e A303921 the main diagonal of which forms this sequence; note that the row sums of A303920 equals A001813(n) = (2*n)!/n!.
%Y A303921 Cf. A303920, A303922.
%K A303921 nonn
%O A303921 0,3
%A A303921 _Paul D. Hanna_, May 02 2018