A266822 Expansion of Product_{k>=1} ((1 + x^k) * (1 + 3*x^k)).

1, 4, 7, 20, 35, 60, 124, 200, 324, 524, 865, 1320, 2016, 3036, 4453, 6684, 9668, 13856, 19792, 27876, 38956, 54640, 75320, 103268, 141191, 191320, 257892, 346164, 463284, 615292, 814883, 1074556, 1409904, 1844284, 2402756, 3118020, 4038164, 5207344, 6694116

Offset

0,2

Comments

Convolution of A000009 and A032308.

Links

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

Formula

a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (4*sqrt(2*Pi) * n^(3/4)), where c = Pi^2/4 + log(3)^2/2 + polylog(2, -1/3) = 2.761842454190822171313479302500904035832... .

Mathematica

nmax = 40; CoefficientList[Series[Product[(1+x^k) * (1+3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000009, A032308, A266819, A266820.

Sequence in context: A084404 A147065 A049947 * A296624 A296663 A066345

Adjacent sequences: A266819 A266820 A266821 * A266823 A266824 A266825

Keyword

nonn

Author

Vaclav Kotesovec, Jan 04 2016

Status

approved