A266819 Expansion of Product_{k>=1} ((1 + x^k) * (1 + 2*x^k)).

1, 3, 5, 12, 20, 33, 60, 93, 144, 222, 340, 498, 729, 1050, 1486, 2115, 2946, 4068, 5592, 7608, 10278, 13854, 18483, 24528, 32426, 42594, 55677, 72498, 94008, 121290, 156002, 199842, 255012, 324438, 411318, 519771, 655128, 823056, 1031148, 1288590, 1605945

Offset

0,2

Comments

Convolution of A000009 and A032302.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Formula

a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2*sqrt(6*Pi)*n^(3/4)), where c = Pi^2/4 + log(2)^2/2 + polylog(2, -1/2) = 2.259213400307794164599109607216595948859... .

Mathematica

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

Crossrefs

Cf. A000009, A032302, A266820, A266822.

Sequence in context: A024458 A143643 A321679 * A245939 A089292 A309702

Adjacent sequences: A266816 A266817 A266818 * A266820 A266821 A266822

Keyword

nonn

Author

Vaclav Kotesovec, Jan 04 2016

Status

approved