A269153 Expansion of Product_{k>=1} ((1 - k*x^k) / (1 - 2*x^k)).

1, 1, 2, 3, 5, 9, 15, 33, 62, 130, 264, 554, 1081, 2237, 4483, 8952, 17933, 35921, 71755, 143502, 286713, 573198, 1146540, 2292277, 4584087, 9166802, 18334880, 36668210, 73336840, 146672469, 293348402, 586695560, 1173398119, 2346805311, 4693617598, 9387229673

Offset: 0

Author

Vaclav Kotesovec, Feb 20 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. A070933, A267005, A269144.

Programs

Mathematica

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

Formula

a(n) ~ c * 2^n, where c = Product_{k>=1} (2^k - k)/(2^k - 1) = 0.27320499481666294779155052256744055231134605935215258251663905...