A269154 Expansion of Product_{k>=1} (1 + k*x^k)/(1 + 2*x^k).

1, -1, 2, -3, 9, -13, 31, -53, 118, -210, 452, -866, 1793, -3493, 7119, -13992, 28257, -56253, 113035, -225318, 451745, -901870, 1805976, -3609701, 7222075, -14439594, 28887060, -57763494, 115540784, -231066845, 462154358, -924282660, 1848598423, -3697142099

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..3300

Formula

a(n) ~ c * (-2)^n, where c = Product_{k>=1} ((-2)^k + k)/((-2)^k - 1) = 0.4304067090888734207149852218007129877370867778815471457548443780472...

Mathematica

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

Crossrefs

Cf. A022629, A269144, A269153, A269155.

Sequence in context: A048744 A101234 A233190 * A358829 A225792 A057293

Adjacent sequences: A269151 A269152 A269153 * A269155 A269156 A269157

Keyword

sign

Author

Vaclav Kotesovec, Feb 20 2016

Status

approved