A370243 Coefficient of x^n in the expansion of ( 1/(1-x) * (1+x^2)^2 )^n.
1, 1, 7, 28, 143, 701, 3580, 18376, 95471, 499231, 2626607, 13883904, 73681316, 392323868, 2094932728, 11214085328, 60157698287, 323325959395, 1740682221829, 9385343934124, 50671846382743, 273913020523933, 1482311190765896, 8029798017622048, 43538300361416708
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)*binomial((u+1)*n-s*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(2*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)^2 ). See A369226.