A370195 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x^2)^2 )^n.
1, 2, 10, 56, 322, 1902, 11440, 69680, 428418, 2653292, 16527910, 103443144, 649964176, 4097464490, 25904239560, 164168677056, 1042651014018, 6634470805556, 42286359318364, 269925368946896, 1725325033144622, 11041442722096094, 70739175615642016
Offset: 0
Programs
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Mathematica
a[n_]:=SeriesCoefficient[((1+x)^2*(1+x^2)^2)^n,{x,0,n}]; Array[a,23,0] (* Stefano Spezia, Apr 30 2024 *) -
PARI
a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(2*n,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)^2 * (1+x^2)^2) ). See A369441.