A258788 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)).

1, 1, 3, 12, 47, 192, 811, 3539, 15765, 71362, 327748, 1524081, 7161629, 33958506, 162312471, 781305581, 3784573140, 18435578714, 90261022638, 443956543235, 2192796266004, 10872208762458, 54095648185434, 270029668955605, 1351943521270155, 6787479872751732

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..494

Crossrefs

Cf. A258234, A258789, A258797.

Programs

Maple

T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n
				

Mathematica

Table[SeriesCoefficient[1/Product[x^k*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(n+3)/2}], {n, 0, 30}]

Formula

a(n) ~ c * d^n / n^2, where d = A258234 = 5.40087190411815415246609111910427005202943771019167057093170601448448... = r^2/(r-1), where r is the root of the equation polylog(2, 1-r) + log(r)^2 = 0, c = 2.578341962163260914344332458898614289944... .