A270923 Coefficient of x^n in Product_{k>=1} ((1 + x^k) / (1 - x^k))^(k^n).

1, 2, 10, 88, 1414, 46648, 3026028, 373615284, 92794268694, 46265940243794, 44694344296430280, 86689242777435107120, 340600515192402995860548, 2624923513793602103874986688, 40749869155795866122979193705136, 1290021269710020392957588463834452744

Offset: 0

Author

Vaclav Kotesovec, Mar 26 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A252782, A270917, A270919, A270924.

Programs

Mathematica

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

Formula

Conjecture: limit n->infinity a(n)^(1/n^2) = exp(exp(-1)) = 1.444667861...

a(n) = [x^n] exp(Sum_{k>=1} (sigma_(n+1)(2*k) - sigma_(n+1)(k))*x^k/(2^n*k)). - Ilya Gutkovskiy, Apr 26 2019