A293302 E.g.f.: Product_{m>0} 1/(1 - x^m + x^(2*m)/2!).

1, 1, 3, 12, 66, 450, 3510, 32760, 335160, 3832920, 48648600, 673596000, 9961736400, 161026866000, 2775402630000, 50713246584000, 987048958896000, 20331148966128000, 440625863806128000, 10057578887708352000, 240218186856167520000, 6010719623406257760000

Offset: 0

Author

Seiichi Manyama, Oct 05 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..444

Crossrefs

Column k=2 of A293301.

Cf. A003105.

Programs

Mathematica

nmax = 25; CoefficientList[Series[1/Product[1 - x^k + x^(2*k)/2, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 05 2017 *)

PARI

my(x = 'x + O('x^40)); Vec(serlaplace(prod(m=1, 40, 1/(1 - x^m + x^(2*m)/2!)))) \\ Michel Marcus, Oct 05 2017

Formula

a(n) ~ (5*Pi^2/3 - 4*log(2)^2)^(1/4) * n^(n - 1/4) / (4*exp(n - sqrt((5*Pi^2/12 - log(2)^2)*n))). - Vaclav Kotesovec, Oct 07 2024