A292424 a(n) = [x^n] Product_{k=1..n} 1/((1 - x)^k * (1 - x^k)).

1, 2, 11, 92, 1080, 16490, 311238, 7007796, 183431836, 5474465390, 183502419505, 6825981504602, 279041903645153, 12434720809043056, 599929817745490600, 31155278025923406979, 1732781419647450834768, 102761486514549541577999, 6473124665688520200808139

Offset: 0

Author

Vaclav Kotesovec, Sep 20 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..368

Crossrefs

Cf. A292613.

Programs

Mathematica

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

PARI

{a(n)= polcoef(prod(k=1, n, 1/((1-x)^k*(1-x^k) +x*O(x^n))), n)};
for(n=0,20, print1(a(n), ", ")) \\ G. C. Greubel, Feb 02 2019

Formula

a(n) ~ exp(n+2) * n^(n-1/2) / (sqrt(Pi) * 2^(n+1/2)).