A366645 G.f. A(x) satisfies A(x) = 1 + x^3 * (A(x) / (1 - x))^4.
1, 0, 0, 1, 4, 10, 24, 67, 200, 586, 1704, 5049, 15232, 46284, 141240, 433696, 1340500, 4164830, 12993792, 40697472, 127941300, 403561902, 1276763096, 4050430502, 12882398456, 41068966204, 131211997496, 420056152498, 1347272602056, 4328764460928, 13931034024536
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n+k-1, n-3*k)*binomial(4*k, k)/(3*k+1));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,n-3*k) * binomial(4*k,k) / (3*k+1).