A277029 - OEIS

%I #18 Feb 16 2021 21:18:55

%S 0,1,4,8,16,25,42,61,90,130,178,242,332,436,566,747,952,1210,1540,

%T 1926,2400,2994,3674,4506,5526,6708,8108,9808,11768,14080,16850,20022,

%U 23738,28128,33152,39015,45854,53662,62696,73166,85118,98826,114636,132586,153102

%N Convolution of A000203 and A000009.

%C Apart from initial zero this is the convolution of A340793 and A036469. - _Omar E. Pol_, Feb 16 2021

%H Vaclav Kotesovec, <a href="/A277029/b277029.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%t Table[Sum[DivisorSigma[1, k] * PartitionsQ[n-k], {k,1,n}], {n,0,50}]

%t 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]

%Y Cf. A066186 (convolution of A000203 and A000041).

%Y Cf. A276432 (convolution of A000203 and A000219).

%Y Cf. A066189, A036469, A340793.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Sep 25 2016