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A277029 Convolution of A000203 and A000009. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

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

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Last modified March 22 01:06 EDT 2019. Contains 321406 sequences. (Running on oeis4.)