A370617 Coefficient of x^n in the expansion of 1 / (1-x-x^2)^(2*n).
1, 2, 14, 98, 726, 5522, 42770, 335512, 2656998, 21195944, 170076214, 1371181110, 11098310730, 90128497032, 734008622872, 5992486341248, 49028047353670, 401885885751630, 3299812135410080, 27134786911366212, 223433635272820126, 1842041118321640390
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=2, u=0) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(3*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-x^2)^2 ). See A368961.