A397056 - OEIS

%I #8 Jun 15 2026 09:07:36

%S 0,1,4,9,22,44,92,175,330,606,1076,1891,3258,5526,9236,15291,24964,

%T 40393,64728,102791,161930,253184,392978,605924,928466,1414066,

%U 2141696,3226409,4835794,7212968,10709434,15830353,23301798,34161140,49887096,72581655,105222878,152017339,218893288

%N Convolution of A000203 and A026007.

%H Vaclav Kotesovec, <a href="/A397056/b397056.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)^k.

%F a(n) ~ Pi^(3/2) * exp(3^(4/3)*zeta(3)^(1/3)*n^(2/3)/2^(4/3)) / (9 * 2^(13/12) * zeta(3)^(1/2)).

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

%Y Cf. A000203, A026007.

%Y Cf. A276432, A397057.

%Y Cf. A066186, A277029, A335651.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jun 15 2026