A321262 Expansion of 1/(1 - Sum_{k>=1} k*x^(2*k)/(1 - x^k)).

1, 0, 1, 1, 4, 3, 14, 12, 43, 50, 140, 177, 474, 643, 1560, 2325, 5246, 8194, 17763, 28838, 60190, 101063, 204935, 352227, 700037, 1224816, 2394971, 4250616, 8209174, 14724570, 28175997, 50949079, 96797183, 176131780, 332804667, 608449008, 1144920041, 2100793404

Offset

0,5

Comments

Invert transform of A001065.

Links

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

N. J. A. Sloane, Transforms

Formula

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

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

a(0) = 1; a(n) = Sum_{k=1..n} A001065(k)*a(n-k).

Maple

a:=series(1/(1-add(k*x^(2*k)/(1-x^k), k=1..100)), x=0, 38): seq(coeff(a, x, n), n=0..37); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 37; CoefficientList[Series[1/(1 - Sum[k x^(2 k)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 37; CoefficientList[Series[1/(1 - Sum[(k - EulerPhi[k]) x^k/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(DivisorSigma[1, k] - k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 37}]

Crossrefs

Cf. A001065, A180305, A318784, A319107, A320651, A321263.

Sequence in context: A351992 A082383 A216486 * A056478 A056479 A056480

Adjacent sequences: A321259 A321260 A321261 * A321263 A321264 A321265

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 01 2018

Status

approved