cp's OEIS Frontend

A238000 Number of partitions of n^n into parts that are at most n.

%I A238000 #19 Nov 03 2018 17:19:56
%S A238000 0,1,3,75,123464,33432635477,2561606354507677872,
%T A238000 85980297709044488588773397089,
%U A238000 1841159754991692001851990839259642586671980,34687845413783594101366282545316028561007822069601179170488
%N A238000 Number of partitions of n^n into parts that are at most n.
%H A238000 Alois P. Heinz, <a href="/A238000/b238000.txt">Table of n, a(n) for n = 0..27</a>
%H A238000 A. V. Sills and D. Zeilberger, <a href="https://arxiv.org/abs/1108.4391">Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)</a> (arXiv:1108.4391 [math.CO])
%F A238000 a(n) = [x^(n^n)] Product_{j=1..n} 1/(1-x^j).
%F A238000 a(n) ~ exp(2*n) * n^(n*(n-3)) / (2*Pi). - _Vaclav Kotesovec_, May 25 2015
%e A238000 a(1) = 1: 1.
%e A238000 a(2) = 3: 22, 211, 1111.
%e A238000 a(3) = 75: 333333333, ..., 111111111111111111111111111.
%t A238000 a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, n^n}];
%t A238000 a[0] = 0;
%t A238000 Table[a[n], {n, 0, 5}] (* _Jean-François Alcover_, Nov 03 2018 *)
%Y A238000 Main diagonal of A238010 and A238016.
%Y A238000 Cf. A236810, A237512, A237998, A237999, A238001.
%K A238000 nonn
%O A238000 0,3
%A A238000 _Alois P. Heinz_, Feb 16 2014