A372411 Coefficient of x^n in the expansion of ( (1-x+x^2)^2 / (1-x)^3 )^n.
1, 1, 7, 34, 183, 1001, 5578, 31459, 179063, 1026493, 5918007, 34277728, 199309146, 1162682314, 6801575641, 39885002534, 234384591991, 1379936226605, 8137835460115, 48062073927739, 284233390132183, 1682950066882489, 9975692904121556, 59190095764321975
Offset: 0
Keywords
Programs
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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));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(2*n-k-1,n-2*k).
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.