A371313 Expansion of e.g.f. Product_{k>=1} 1 / (1 - x^k/k)^2.
1, 2, 8, 40, 254, 1868, 15996, 153144, 1637520, 19191072, 245463936, 3390905472, 50406479328, 800678811840, 13547088596544, 242995426574976, 4607744279916672, 92046384885051648, 1932579234508861440, 42530614791735573504, 979132781170084872960, 23529915213836747927040
Offset: 0
Keywords
Programs
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Mathematica
nmax = 21; CoefficientList[Series[Product[1/(1 - x^k/k)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(n) ~ exp(-2*gamma) * n! * n^3 / 6, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 24 2024
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