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A321190 a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^k/(1 - x^k)). 1
1, 1, 6, 47, 778, 25476, 1752936, 242632397, 70015221566, 41446777283255, 49999934258165654, 125272856707074638221, 641938223803783115191706, 6731818441446626626586172740, 146378489075644780343627471981694, 6505906463580477520696075719916583118 (list; graph; refs; listen; history; text; internal format)
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: A307567 A332238 A192887 * A320403 A323138 A000252

Adjacent sequences:  A321187 A321188 A321189 * A321191 A321192 A321193

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 29 2018

STATUS

approved

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Last modified July 8 08:08 EDT 2020. Contains 335520 sequences. (Running on oeis4.)