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

0,3

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

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)).

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]

Crossrefs

Cf. A066186 (convolution of A000203 and A000041).

Cf. A276432 (convolution of A000203 and A000219).

Cf. A066189, A036469, A340793.

Sequence in context: A290190 A193452 A003451 * A013934 A167189 A050470

Adjacent sequences: A277026 A277027 A277028 * A277030 A277031 A277032

Keyword

nonn

Author

Vaclav Kotesovec, Sep 25 2016

Status

approved