A372462 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^2)^2 )^n.
1, 3, 17, 105, 673, 4403, 29183, 195170, 1313889, 8889963, 60392717, 411615867, 2813115487, 19270525316, 132273530462, 909530996780, 6263834506593, 43198661550219, 298296958413785, 2062180461738075, 14271253423675773, 98859742466265935
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, 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/2)} (-1)^k * binomial(2*n+k-1,k) * binomial(4*n-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+x^2)^2 ). See A368973.