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A293302
E.g.f.: Product_{m>0} 1/(1 - x^m + x^(2*m)/2!).
2
1, 1, 3, 12, 66, 450, 3510, 32760, 335160, 3832920, 48648600, 673596000, 9961736400, 161026866000, 2775402630000, 50713246584000, 987048958896000, 20331148966128000, 440625863806128000, 10057578887708352000, 240218186856167520000, 6010719623406257760000
OFFSET
0,3
LINKS
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
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 *)
PROG
(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
CROSSREFS
Column k=2 of A293301.
Cf. A003105.
Sequence in context: A267323 A058790 A199746 * A248871 A080599 A349581
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 05 2017
STATUS
approved