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

0,2

Links

Table of n, a(n) for n=0..20.

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).

Prog

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

Crossrefs

Cf. A005809, A024485, A075436, A370327, A370376.

Sequence in context: A163473 A063979 A308354 * A361841 A361880 A073978

Adjacent sequences: A370372 A370373 A370374 * A370376 A370377 A370378

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 16 2024

Status

approved