A304989 G.f.: Sum_{k>=0} A000041(k)^2 * x^k / Sum_{k>=0} A000009(k)^2 * x^k.

1, 0, 3, 2, 16, 10, 59, 32, 187, 90, 519, 152, 1439, 164, 3525, -246, 8904, -2500, 21748, -10836, 53918, -36508, 131424, -115266, 328703, -336608, 812615, -957464, 2046225, -2634166, 5152190, -7145682, 13121677, -19039178, 33473773, -50395004, 86035125

Offset

0,3

Links

Table of n, a(n) for n=0..36.

Formula

a(n) ~ (-1)^n * c * d^n, where d = 1.6096199212376592810929072080593393678131347423108390218672748044914523428584..., c = 3.049014588253509415528984781833089943634060493523166258285691300445092167...

Mathematica

nmax = 50; CoefficientList[Series[Sum[PartitionsP[k]^2*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]^2*x^k, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000009, A000041, A001255, A054440, A304877, A304990.

Sequence in context: A084886 A275463 A338280 * A055864 A209600 A072045

Adjacent sequences: A304986 A304987 A304988 * A304990 A304991 A304992

Keyword

sign

Author

Vaclav Kotesovec, May 23 2018

Status

approved