A370376 Number of compositions of n where there are A025174(k) sorts of part k.
1, 1, 6, 39, 262, 1791, 12372, 86052, 601374, 4217151, 29648766, 208855791, 1473509736, 10408539844, 73596075552, 520797997464, 3687846866382, 26128671296127, 185209915856802, 1313356295909877, 9316374980571702, 66105343198654407, 469174119885678972
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, binomial(3*k, k)*x^k)/3))
Formula
G.f.: 1 / (1 - 1/3 * Sum_{k>=1} binomial(3*k,k) * x^k).
a(0) = 1; a(n) = 1/3 * Sum_{k=1..n} binomial(3*k,k) * a(n-k).