A293302 - OEIS

%I #26 Oct 07 2024 18:08:19

%S 1,1,3,12,66,450,3510,32760,335160,3832920,48648600,673596000,

%T 9961736400,161026866000,2775402630000,50713246584000,987048958896000,

%U 20331148966128000,440625863806128000,10057578887708352000,240218186856167520000,6010719623406257760000

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

%H Seiichi Manyama, <a href="/A293302/b293302.txt">Table of n, a(n) for n = 0..444</a>

%F 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

%t 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 *)

%o (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

%Y Column k=2 of A293301.

%Y Cf. A003105.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 05 2017