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%I #11 Apr 30 2024 06:06:03
%S 1,1,7,34,183,1001,5578,31459,179063,1026493,5918007,34277728,
%T 199309146,1162682314,6801575641,39885002534,234384591991,
%U 1379936226605,8137835460115,48062073927739,284233390132183,1682950066882489,9975692904121556,59190095764321975
%N Coefficient of x^n in the expansion of ( (1-x+x^2)^2 / (1-x)^3 )^n.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(2*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)^3 / (1-x+x^2)^2 ). See A369229.
%o (PARI) a(n, s=2, t=2, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A092765, A369229.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 29 2024
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