A371612 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^2) )^2.
1, 2, 3, 12, 49, 218, 1037, 5106, 25909, 134410, 709691, 3801498, 20606654, 112828202, 623087675, 3466539248, 19411070496, 109313442562, 618713495451, 3517737628368, 20081523836403, 115058714898196, 661432784830204, 3813891082337178, 22052422636145522
Offset: 0
Keywords
Programs
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PARI
a(n, r=2, s=1, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Formula
a(n) = Sum_{k=0..n} binomial(4*(n-k)+2,k) * binomial(n-1,n-k)/(2*(n-k)+1).