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A307242
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*sigma_2(k+1)*a(n-k), where sigma_2() is the sum of squares of divisors (A001157).
1
1, 5, 15, 46, 159, 570, 2036, 7208, 25400, 89456, 315335, 1112286, 3923867, 13841052, 48818892, 172186234, 607314043, 2142064478, 7555322206, 26648517536, 93992371863, 331521717928, 1169314641890, 4124305724658, 14546896171716, 51308559972146, 180971133233105, 638305788168090
OFFSET
0,2
FORMULA
G.f.: -x / Sum_{k>=1} k^2*(-x)^k/(1 - (-x)^k).
G.f.: 1 / (d/dx) log(Product_{k>=1} (1 - (-x)^k)^k).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) DivisorSigma[2, k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 27}]
nmax = 27; CoefficientList[Series[-x/Sum[k^2 (-x)^k/(1 - (-x)^k), {k, 1, nmax + 1}], {x, 0, nmax}], x]
nmax = 27; CoefficientList[Series[1/D[Log[Product[(1 - (-x)^k)^k, {k, 1, nmax + 1}]], x], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 30 2019
STATUS
approved