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A320649
Expansion of 1/(1 - Sum_{k>=1} k^2*x^k/(1 - x^k)).
5
1, 1, 6, 21, 82, 294, 1116, 4103, 15326, 56833, 211454, 785441, 2920058, 10851016, 40331874, 149892024, 557098510, 2070493098, 7695228038, 28600012305, 106294901116, 395055313662, 1468262641770, 5456942875386, 20281270503914, 75377349437075, 280147395367820
OFFSET
0,3
COMMENTS
Invert transform of A001157.
LINKS
N. J. A. Sloane, Transforms
FORMULA
G.f.: 1/(1 + x * (d/dx) log(Product_{k>=1} (1 - x^k)^k)).
a(0) = 1; a(n) = Sum_{k=1..n} sigma_2(k)*a(n-k).
MAPLE
a:=series(1/(1-add(k^2*x^k/(1-x^k), k=1..100)), x=0, 27): seq(coeff(a, x, n), n=0..26); # Paolo P. Lava, Apr 02 2019
MATHEMATICA
nmax = 26; CoefficientList[Series[1/(1 - Sum[k^2 x^k/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 26; CoefficientList[Series[1/(1 + x D[Log[Product[(1 - x^k)^k, {k, 1, nmax}]], x]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[DivisorSigma[2, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 26}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 18 2018
STATUS
approved