A304988 G.f.: Sum_{k>=0} A000041(k)^2 * x^k / Sum_{k>=0} A000009(k) * x^k.

1, 0, 3, 4, 16, 20, 67, 84, 231, 324, 735, 1026, 2265, 3086, 6199, 8880, 16564, 23390, 42378, 59496, 103588, 146376, 244278, 344186, 564013, 788168, 1255201, 1758400, 2738833, 3812242, 5846114, 8092092, 12200957, 16848156, 24991705, 34365176, 50392543

Offset

0,3

Links

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

Formula

a(n) ~ 7^(3/2) * exp(Pi*sqrt(7*n/3)) / (768*n^2).

Mathematica

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

Crossrefs

Cf. A000009, A000041, A001255, A054440, A304877, A305350.

Sequence in context: A334319 A330299 A047164 * A108653 A316194 A123773

Adjacent sequences: A304985 A304986 A304987 * A304989 A304990 A304991

Keyword

nonn

Author

Vaclav Kotesovec, May 23 2018

Status

approved