A367236 G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^2)^2.
1, 1, 2, 7, 26, 107, 462, 2074, 9572, 45147, 216638, 1054254, 5190710, 25810064, 129423512, 653740518, 3323270096, 16988894131, 87283137130, 450434292624, 2333851816654, 12136369892776, 63318984098996, 331347363084737, 1738713937163124, 9146850725274636
Offset: 0
Keywords
Programs
-
PARI
a(n, s=2, t=0, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
Formula
If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).