A261563 Expansion of Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^k.

1, 4, 16, 60, 192, 596, 1744, 4892, 13248, 34868, 89296, 223660, 548928, 1323060, 3137520, 7332332, 16907584, 38517444, 86777328, 193523404, 427562816, 936555044, 2035286576, 4390850268, 9409096576, 20037827876, 42429318480, 89369282460, 187325508288

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ c * 2^n, where c = 2 * Product_{j>=1} ((1 + 1/2^j)/(1 - 1/2^j))^(j+1) = 1021.5383556752320172813996404366861329314041364322798995039038143325883...

G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} (2^d - (-2)^d) * n^2/d^2 ). - Paul D. Hanna, Sep 30 2015

Mathematica

nmax = 50; CoefficientList[Series[Product[((1 + 2*x^k)/(1 - 2*x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[Exp[Sum[2^(2*k)/(2*k-1)*x^(2*k-1)/(1 - x^(2*k-1))^2, {k, 1, nmax}]], {x, 0, nmax}], x]

Prog

(PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, (2^d - (-2)^d) * m^2/d^2) ) +x*O(x^n)), n)}
for(n=0, 40, print1(a(n), ", ")) \\ Paul D. Hanna, Sep 30 2015

Crossrefs

Cf. A156616, A261561, A261562, A261584.

Sequence in context: A374096 A032094 A282083 * A265955 A217374 A055295

Adjacent sequences: A261560 A261561 A261562 * A261564 A261565 A261566

Keyword

nonn

Author

Vaclav Kotesovec, Aug 24 2015

Status

approved