A370618 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^2 )^n.
1, 1, 7, 34, 191, 1071, 6154, 35729, 209455, 1236508, 7341577, 43792112, 262230242, 1575391156, 9490934411, 57316715079, 346875036879, 2103174805035, 12773139313516, 77689736488088, 473160660856361, 2885208137132852, 17612514244078288, 107621658416373752
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=2, u=1) = sum(k=0, n\s, 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)} binomial(2*n+k-1,k) * binomial(2*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-x^2)^2 / (1-x) ). See A369486.