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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

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

Cf. A001157, A002039, A307241, A320649.

Sequence in context: A079798 A037504 A197237 * A296545 A089040 A331237

Adjacent sequences:  A307239 A307240 A307241 * A307243 A307244 A307245

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 30 2019

STATUS

approved

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Last modified January 16 06:41 EST 2021. Contains 340204 sequences. (Running on oeis4.)