A376547 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)*A(x)^3.
1, 0, 0, 1, 1, 0, 3, 6, 3, 12, 36, 36, 67, 220, 330, 493, 1420, 2730, 4158, 9933, 21693, 36312, 75684, 171360, 316011, 617424, 1374156, 2723667, 5256237, 11303028, 23362779, 45734304, 95506488, 200821140, 401891490, 825565455, 1739179533, 3549322296
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(k, n-3*k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(k,n-3*k) * binomial(3*k,k)/(2*k+1).