A293182 Expansion of Product_{k>=1} (1 + 2*x^k - x^(2*k)).

1, 2, 1, 6, 3, 6, 16, 12, 16, 22, 51, 36, 60, 62, 91, 154, 148, 176, 236, 278, 328, 552, 508, 670, 771, 988, 1068, 1438, 1844, 1998, 2401, 2882, 3300, 4030, 4640, 5406, 7212, 7584, 9072, 10480, 12612, 13964, 17024, 18860, 22545, 27298, 30340, 34372, 41068

Offset: 0

Author

Vaclav Kotesovec, Oct 01 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A162891, A263401, A276527, A293138.

Programs

Maple

N:= 100:
P:= mul(1+2*x^m- x^(2*m), m=1..N):
S:= series(P,x,N+1):
seq(coeff(S,x,n), n=0..N); # Robert Israel, Oct 01 2017

Mathematica

nmax = 100; CoefficientList[Series[Product[1+2*x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2^(3/2) * sqrt(Pi) * n^(3/4)), where c = Pi^2/6 + log(1+sqrt(2))^2/2 + polylog(2, 3-2*sqrt(2))/2 - 2*polylog(2, sqrt(2)-1) = 1.18805291660775259061867850175092520191179528961165451864292...