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, 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

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: A344814 A037504 A197237 * A296545 A089040 A331237

Adjacent sequences: A307239 A307240 A307241 * A307243 A307244 A307245

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 30 2019

Status

approved