A396891 - OEIS

%I #7 Jun 09 2026 10:11:50

%S 0,1,6,18,52,120,288,602,1280,2538,5000,9449,17748,32305,58338,103185,

%T 180752,311678,532818,899270,1505560,2494674,4102450,6688009,10828656,

%U 17400825,27787370,44081766,69530552,109028748,170068890,263881579,407469728,626174109,957982470,1459186610

%N Convolution of A001157 and A000219.

%F G.f.: Sum_{j>=1} (j^2*x^j/(1-x^j)) / Product_{k>=1} (1-x^k)^k.

%F a(n) ~ zeta(3)^(7/36) * exp(1/12 + 3*zeta(3)^(1/3)*n^(2/3)/2^(2/3)) * n^(11/36) / (A * 2^(11/36) * sqrt(3*Pi)), where A is the Glaisher-Kinkelin constant (A074962).

%t nmax = 40; CoefficientList[Series[Sum[j^2*x^j/(1-x^j),{j,1,nmax}] / Product[(1-x^k)^k, {k,1,nmax}], {x, 0, nmax}], x]

%Y Cf. A001157, A000219, A074962, A276432.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jun 09 2026