A347829 a(n) = Sum_{k=0..n} 2^k * A000041(k) * A000009(n-k).

1, 3, 11, 36, 118, 351, 1082, 3093, 8984, 25164, 70434, 191808, 525559, 1404672, 3755506, 9906111, 26057062, 67703310, 175745506, 451392114, 1157272780, 2944110060, 7468477985, 18821686554, 47337840114, 118344795738, 295156919969, 732694232394, 1814357671094

Offset: 0

Author

Vaclav Kotesovec, Sep 15 2021

Keywords

• nonn

Crossrefs

Cf. A000009, A000041, A015128, A079555, A264685, A347830.

Programs

Mathematica

Table[Sum[2^k*PartitionsP[k]*PartitionsQ[n-k], {k, 0, n}], {n, 0, 50}]
nmax = 50; CoefficientList[Series[Product[(1 + x^k) / (1 - 2^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ A079555 * 2^n * A000041(n).

a(n) ~ QPochhammer(-1/2, 1/2) * 2^(n-2) * exp(Pi*sqrt(2*n/3)) / (sqrt(3)*n).

G.f.: Product_{k>=1} (1 + x^k) / (1 - 2^k*x^k).