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%I #7 May 02 2024 09:46:32
%S 1,4,40,442,5136,61424,748462,9240480,115194720,1446820588,
%T 18279806600,232071505120,2958062657550,37831613904036,
%U 485233557808704,6239148779539472,80397210629541696,1037970502613332320,13423439565585274180,173859642721737225552
%N Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2) )^(2*n).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(5*n-k-1,n-2*k).
%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^2)^2 ). See A368967.
%o (PARI) a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A368967, A372233, A372464.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 01 2024
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