A326858 E.g.f.: Product_{k>=1} (1 + x^(3*k-2) / (3*k-2)).
1, 1, 0, 0, 6, 30, 0, 720, 5760, 0, 362880, 5417280, 17107200, 479001600, 8885479680, 32691859200, 1307674368000, 34151856076800, 214585052774400, 6402373705728000, 192796754895360000, 1542202547010048000, 55105230485200896000, 1944933030182596608000
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..440
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[(1+x^(3*k-2)/(3*k-2)), {k, 1, Floor[nmax/3]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
Formula
a(n) ~ n! / (3^(1/3) * Gamma(2/3) * exp(gamma/3) * n^(2/3)), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function.