A379087 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(3*n+k,n-3*k).
1, 3, 15, 93, 651, 4803, 36177, 275208, 2108091, 16243671, 125817345, 978933354, 7646000421, 59915086026, 470820659940, 3708756501018, 29276677544619, 231540519752376, 1834228504348863, 14552075416977531, 115605043235217081, 919503729585453147
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(3*n+k-1, k)*binomial(3*n+k, n-3*k));
Formula
a(n) = [x^n] 1/( 1/(1 + x) - x^3 )^(3*n).
a(n) == 0 (mod 3) for n>0.