A346452 a(n) = [x^n] Product_{k>=1} (1 + n^(k-1)*x^k) / (1 - n^(k-1)*x^k).

1, 2, 6, 32, 242, 2472, 31850, 490912, 8897058, 185373722, 4344896842, 113667973344, 3283155709106, 103486639506824, 3544144942010010, 131038318999642112, 5192873357864667202, 219952910549005233840, 9916266932124308092586, 473513072853351852164160

Offset: 0

Author

Vaclav Kotesovec, Jul 19 2021

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A340103, A338697, A346454.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 + n^(k - 1)*x^k)/(1 - n^(k - 1)*x^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[SeriesCoefficient[2*x + (n - 1)/(n + 1)*QPochhammer[-1/n, n*x]/QPochhammer[1/n, n*x], {x, 0, n}], {n, 1, 20}]]

Formula

a(n) ~ c * n^(n-1), where c = sqrt(2) * BesselI(1, 2*sqrt(2)) = 4.78966619...