A269144 Expansion of Product_{k>=1} ((1 + k*x^k) / (1 - 2*x^k)).

1, 3, 10, 29, 77, 195, 475, 1115, 2546, 5706, 12528, 27106, 57893, 122299, 255995, 531816, 1097377, 2252151, 4600835, 9362334, 18990645, 38418370, 77548880, 156251955, 314363615, 631703790, 1268148900, 2543812090, 5099469848, 10217529291, 20464112218

Offset: 0

Author

Vaclav Kotesovec, Feb 20 2016

Keywords

• nonn

Comments

Convolution of A022629 and A070933.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..3290

Crossrefs

Cf. A022629, A070933, A267004, A269153.

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) = 19.14883592186082265751161402244824703642181055238186925199088...