A370621 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^3 )^n.
1, 2, 16, 119, 948, 7732, 64231, 540311, 4588076, 39244106, 337624066, 2918384229, 25325306031, 220497804256, 1925231880973, 16850975055139, 147807248526268, 1298926641563548, 11434042768577866, 100800817171002817, 889839745865544598
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[((1-x)/(1-x-x^2)^3)^n,{x,0,n}]; Array[a,21,0] (* Stefano Spezia, May 01 2024 *) -
PARI
a(n, s=2, t=3, u=1) = 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(3*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)^3 / (1-x) ). See A369487.