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

Author

Olivier Gérard

Keywords

• nonn

Links

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

Crossrefs

Cf. A062796.

Programs

Magma

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

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 *)

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

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