OFFSET
0,3
FORMULA
G.f.: 1/(1 - Sum_{k>=1} k*x^k/(1 - x^k)^2).
G.f.: 1/(1 - Sum_{k>=1} k*d(k)*x^k), where d(k) = number of divisors of k (A000005).
a(0) = 1; a(n) = Sum_{k=1..n} A038040(k)*a(n-k).
a(n) ~ c / r^n, where r = 0.304499876501217750838861744045680232405337905509126... is the root of the equation Sum_{k>=1} k*r^k/(1 - r^k)^2 = 1 and c = 0.44152042515136849968144466258954953693306684400261343177792428746297872748... - Vaclav Kotesovec, Aug 28 2018
MAPLE
a:=series(1/(1-add(add(i*j*x^(i*j), j=1..100), i=1..100)), x=0, 30): seq(coeff(a, x, n), n=0..29); # Paolo P. Lava, Apr 02 2019
MATHEMATICA
nmax = 29; CoefficientList[Series[1/(1 - Sum[Sum[i j x^(i j), {i, 1, nmax}], {j, 1, nmax}]), {x, 0, nmax}], x]
nmax = 29; CoefficientList[Series[1/(1 - Sum[k x^k/(1 - x^k)^2, {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 29; CoefficientList[Series[1/(1 - Sum[k DivisorSigma[0, k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[k DivisorSigma[0, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 29}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 27 2018
STATUS
approved