A277029 Convolution of A000203 and A000009.

0, 1, 4, 8, 16, 25, 42, 61, 90, 130, 178, 242, 332, 436, 566, 747, 952, 1210, 1540, 1926, 2400, 2994, 3674, 4506, 5526, 6708, 8108, 9808, 11768, 14080, 16850, 20022, 23738, 28128, 33152, 39015, 45854, 53662, 62696, 73166, 85118, 98826, 114636, 132586, 153102

Offset: 0

Author

Vaclav Kotesovec, Sep 25 2016

Keywords

• nonn

Comments

Apart from initial zero this is the convolution of A340793 and A036469. - Omar E. Pol, Feb 16 2021

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A066186 (convolution of A000203 and A000041).

Cf. A276432 (convolution of A000203 and A000219).

Cf. A066189, A036469, A340793.

Programs

Mathematica

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

Formula

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

a(n) ~ 2*n*A000009(n) ~ exp(Pi*sqrt(n/3)) * n^(1/4) / (2*3^(1/4)).