A370183 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^3) )^n.
1, 2, 6, 23, 98, 432, 1929, 8689, 39442, 180248, 828376, 3824757, 17727989, 82438852, 384429751, 1797017598, 8417950626, 39506701508, 185718513144, 874346516454, 4121841403488, 19454625634936, 91924347974883, 434783188981384, 2058320844378109, 9752580801216182
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=1, u=1) = 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/3)} binomial(n,k) * binomial(2*n-k,n-3*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) * (1+x+x^3)) ). See A369481.