A023879 Number of partitions in expanding space.

1, 1, 3, 12, 79, 722, 8675, 128177, 2248873, 45644104, 1051632553, 27107038863, 772751427746, 24136897360750, 819689757351091, 30068876227952332, 1184869328943005936, 49914047187427191742

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 A373395

Adjacent sequences: A023876 A023877 A023878 * A023880 A023881 A023882

Keyword

nonn

Author

Olivier Gérard

Status

approved