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

0,3

Links

Table of n, a(n) for n=0..22.

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).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, binomial(3*k, k)*x^k)/3))

Crossrefs

Cf. A005809, A025174, A049027, A370375.

Sequence in context: A238809 A006256 A052392 * A357206 A370026 A199491

Adjacent sequences: A370371 A370372 A370375 * A370377 A370378 A370379

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 16 2024

Status

approved