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A309319
E.g.f.: 1/Product_{k>0} (1 - x^(2*k)/(2*k)) (even powers only).
8
1, 1, 12, 300, 15960, 1232280, 157006080, 25418352960, 5859886032000, 1655203620470400, 604893737678630400, 261278195494386470400, 140231830875916632652800, 86107922772424330377600000, 63316800257542340301112320000, 52666943508290765740968161280000
OFFSET
0,3
LINKS
D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388 (Theorem 6).
FORMULA
a(n) ~ exp(-gamma/2) * (2*n)! / sqrt(n) [Lehmer, 1972], where gamma is the Euler-Mascheroni constant A001620.
MATHEMATICA
nmax = 20; Table[(CoefficientList[Series[1/Product[(1 - x^(2*k)/(2*k)), {k, 1, 2*nmax}], {x, 0, 2*nmax}], x]*Range[0, 2*nmax]!)[[2 n + 1]], {n, 0, nmax}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 23 2019
STATUS
approved