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A023879 Number of partitions in expanding space. 6
1, 1, 3, 12, 79, 722, 8675, 128177, 2248873, 45644104, 1051632553, 27107038863, 772751427746, 24136897360750, 819689757351091, 30068876227952332, 1184869328943005936, 49914047187427191742 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..380

FORMULA

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

G.f.: exp( Sum_{n>=1} A062796(n)/n*x^n ), where A062796(n) = Sum_{d|n} d^d. - Paul D. Hanna, Sep 05 2012

a(n) ~ n^(n-1). - Vaclav Kotesovec, Mar 14 2015

MAPLE

seq(coeff(series(mul((1-x^k)^(-k^(k-1)), k=1..n), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018

MATHEMATICA

nmax=20; CoefficientList[Series[Product[1/(1-x^k)^(k^(k-1)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)

PROG

(PARI) {a(n)=polcoeff(prod(k=1, n, (1-x^k+x*O(x^n))^(-k^(k-1))), n)}

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, d^d)*x^m/m) +x*O(x^n)), n)} \\ Paul D. Hanna, Sep 05 2012

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^(k^(k-1)): k in [1..m]]) )); // G. C. Greubel, Oct 31 2018

CROSSREFS

Cf. A062796.

Sequence in context: A058561 A058107 A213139 * A084565 A323634 A275488

Adjacent sequences:  A023876 A023877 A023878 * A023880 A023881 A023882

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 16 08:15 EDT 2019. Contains 328051 sequences. (Running on oeis4.)