A372463 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^3)^2 )^n.
1, 3, 21, 159, 1261, 10268, 85065, 713345, 6036381, 51438741, 440780736, 3794261496, 32784723361, 284184613586, 2470101750095, 21520640950334, 187885215032925, 1643315666085399, 14396340879235851, 126302446713155886, 1109524512806397656
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=2, u=1) = sum(k=0, n\s, (-1)^k*binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+k-1,k) * binomial(4*n-2*k-1,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)^2 ). See A368974.