A370379 Number of compositions of n where there are (2*k)!/2 sorts of part k.

1, 1, 13, 385, 21061, 1864921, 243833533, 44133789745, 10556951897461, 3223557261840841, 1223184443268467053, 564530822421956927905, 311384269987431969105061, 202282520358685311116600761, 152856358784713560205903602973

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f.: 1 / (1 - Sum(k>=1} (2*k)!/2 * x^k)).

a(0) = 1; a(n) = Sum_{k=1..n} (2*k)!/2 * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, (2*k)!/2*x^k)))

Crossrefs

Cf. A002674, A051295, A370378.

Sequence in context: A329554 A267433 A142122 * A302700 A194489 A354138

Adjacent sequences: A370376 A370377 A370378 * A370380 A370381 A370382

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 17 2024

Status

approved