A307241 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*d(k+1)*a(n-k), where d() is the number of divisors (A000005).

1, 2, 2, 3, 6, 12, 23, 42, 75, 135, 248, 460, 849, 1554, 2837, 5192, 9527, 17490, 32083, 58809, 107781, 197578, 362280, 664320, 1218069, 2233202, 4094289, 7506602, 13763219, 25234674, 46266927, 84828138, 155528132, 285154061, 522819002, 958568628, 1757496665, 3222295912

Offset

0,2

Links

Table of n, a(n) for n=0..37.

Formula

G.f.: -x / Sum_{k>=1} (-x)^k/(1 - (-x)^k).

G.f.: 1 / (d/dx) log(Product_{k>=1} (1 - (-x)^k)^(1/k)).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) DivisorSigma[0, k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 37}]
nmax = 37; CoefficientList[Series[-x/Sum[(-x)^k/(1 - (-x)^k), {k, 1, nmax + 1}], {x, 0, nmax}], x]
nmax = 37; CoefficientList[Series[1/D[Log[Product[(1 - (-x)^k)^(1/k), {k, 1, nmax + 1}]], x], {x, 0, nmax}], x]

Crossrefs

Cf. A000005, A002039, A129921, A307242.

Sequence in context: A049853 A162599 A064319 * A064674 A095902 A103687

Adjacent sequences: A307238 A307239 A307240 * A307242 A307243 A307244

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 30 2019

Status

approved