A370245 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^2)^3 )^n.
1, 2, 16, 110, 828, 6352, 49696, 393668, 3148316, 25362992, 205519616, 1673272702, 13677016932, 112165564656, 922490228032, 7605558361960, 62839438825244, 520180768020464, 4313251202569216, 35818392770702104, 297846498752214128, 2479748570715505472
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=3, u=2) = 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(3*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)^2 / (1+x^2)^3 ). See A369263.