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A255672 Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(k*n). 13
1, 1, 7, 37, 215, 1251, 7459, 44885, 272727, 1668313, 10263057, 63423482, 393440867, 2448542136, 15280435191, 95588065737, 599213418327, 3763242239317, 23673166664695, 149138199543613, 940796936557265, 5941862248557566, 37568309060087582, 237767215209245583 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of partitions of n when parts i are of n*i kinds. - Alois P. Heinz, Nov 23 2018

LINKS

Vaclav Kotesovec and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 501 terms from Vaclav Kotesovec)

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 6.468409145117839606941857350154192468889057616577..., c = 0.25864792865819067933968646380369970564... . - Vaclav Kotesovec, Mar 01 2015

a(n) = [x^n] exp(n*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1, k*add(

      b(n-j, k)*numtheory[sigma][2](j), j=1..n)/n)

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 11 2015

MATHEMATICA

Table[SeriesCoefficient[Product[1/(1-x^k)^(k*n), {k, 1, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 01 2015 *)

CROSSREFS

Cf. A008485, A252782, A270913, A270922.

Main diagonal of A255961.

Sequence in context: A319013 A126475 A274674 * A077239 A046235 A297329

Adjacent sequences:  A255669 A255670 A255671 * A255673 A255674 A255675

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 01 2015

STATUS

approved

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Last modified May 12 05:30 EDT 2021. Contains 343812 sequences. (Running on oeis4.)