A369691 G.f. satisfies A(x) = 1/(1-x)^3 + x^3*A(x)^3.
1, 3, 6, 11, 24, 66, 196, 576, 1692, 5110, 15933, 50604, 161988, 521700, 1693362, 5541679, 18260055, 60487659, 201272437, 672550158, 2256204327, 7596059333, 25655943417, 86904524289, 295154911774, 1004906765178, 3429178160346, 11726499288028, 40178538608682
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n+3*k+2, n-3*k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(n+3*k+2,n-3*k) * binomial(3*k,k) / (2*k+1).