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A326859
E.g.f.: Product_{k>=1} (1 + x^(2*k-1)/(2*k-1)) / (1 - x^(2*k-1)/(2*k-1)).
3
1, 2, 4, 16, 80, 448, 3136, 24512, 218368, 2169600, 23752704, 282882048, 3661787136, 51076644864, 763127316480, 12184024793088, 206679198990336, 3710945850949632, 70379726872117248, 1405297582300200960, 29462283451103182848, 647386758393297371136
OFFSET
0,2
FORMULA
a(n) ~ exp(-gamma) * n * n!, where gamma is the Euler-Mascheroni constant A001620.
MATHEMATICA
nmax = 25; CoefficientList[Series[Product[(1+x^(2*k-1)/(2*k-1))/(1-x^(2*k-1)/(2*k-1)), {k, 1, Floor[nmax/2]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 27 2019
STATUS
approved