A370244 Coefficient of x^n in the expansion of ( 1/(1-x) * (1+x^2)^3 )^n.
1, 1, 9, 37, 221, 1176, 6759, 38368, 222189, 1290367, 7551534, 44367918, 261789647, 1549582126, 9198837384, 54740021712, 326445873389, 1950448508265, 11673082484595, 69965814023259, 419923664517546, 2523379461715576, 15180084331541402, 91411979525372616
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(2*n-2*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) / (1+x^2)^3 ). See A369262.