A372382 Coefficient of x^n in the expansion of ( (1+x+x^2)^4 / (1+x)^3 )^n.
1, 1, 9, 25, 169, 651, 3801, 17053, 93225, 450844, 2396859, 12043494, 63354649, 324888305, 1704137493, 8839907475, 46383701545, 242285478474, 1273274074020, 6681277302239, 35178613785819, 185187072845569, 976888169385302, 5154978257816280, 27240094648199961
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[((1+x+x^2)^4/(1+x)^3)^n,{x,0,n}]; Array[a,25,0] (* Stefano Spezia, Apr 30 2024 *) -
PARI
a(n, s=2, t=4, u=-3) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(4*n,k) * binomial(n-k,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)^4 ). See A372383.