A370375 Number of compositions of n where there are A005809(k) sorts of part k.
1, 3, 24, 201, 1710, 14649, 125934, 1084716, 9353574, 80711625, 696756420, 6016526145, 51962422464, 448833782556, 3877191573720, 33494487646632, 289365173239302, 2499947731531305, 21598513018825920, 186604716462810075, 1612224571249844910
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)))
Formula
G.f.: 1 / (1 - Sum_{k>=1} binomial(3*k,k) * x^k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(3*k,k) * a(n-k).