A378463 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-k-1,n-3*k).
1, 1, 3, 13, 59, 266, 1203, 5489, 25259, 117022, 545038, 2549592, 11970035, 56372460, 266194295, 1259910113, 5975382699, 28390616727, 135108035502, 643891031826, 3072604703774, 14679493913048, 70206875750168, 336103001918788, 1610476039036259, 7723148579525441
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(2*n-k-1, n-3*k));
Formula
a(n) = [x^n] 1/(1 - x - x^3/(1 - x))^n.