A321190 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^k/(1 - x^k)).

1, 1, 6, 47, 778, 25476, 1752936, 242632397, 70015221566, 41446777283255, 49999934258165654, 125272856707074638221, 641938223803783115191706, 6731818441446626626586172740, 146378489075644780343627471981694, 6505906463580477520696075719916583118

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = [x^n] 1/(1 - Sum_{k>=1} sigma_n(k)*x^k).

a(n) = [x^n] 1/(1 - Sum_{i>=1, j>=1} j^n*x^(i*j)).

a(n) = [x^n] 1/(1 + x * (d/dx) log(Product_{k>=1} (1 - x^k)^(k^(n-1)))).

Maple

seq(coeff(series((1-add(k^n*x^k/(1-x^k), k=1..n))^(-1), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 29 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[k^n x^k/(1 - x^k), {k, 1, n}]), {x, 0, n}], {n, 0, 15}]
Table[SeriesCoefficient[1/(1 - Sum[DivisorSigma[n, k] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 15}]
Table[SeriesCoefficient[1/(1 - Sum[Sum[j^n x^(i j), {j, 1, n}], {i, 1, n}]), {x, 0, n}], {n, 0, 15}]

Crossrefs

Cf. A023887, A129921, A180305, A319647, A320649, A321042.

Sequence in context: A332238 A353548 A192887 * A320403 A354067 A357430

Adjacent sequences: A321187 A321188 A321189 * A321191 A321192 A321193

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 29 2018

Status

approved