cp's OEIS Frontend

A237998 Number of partitions of 2^n into parts that are at most n.

%I A237998 #20 Nov 03 2018 18:46:53
%S A237998 0,1,3,10,64,831,26207,2239706,567852809,454241403975,
%T A237998 1192075219982204,10510218491798860052,315981966712495811700951,
%U A237998 32726459268483342710907384794,11771239570056489326716955796095261,14808470136486015545654676685321653888199
%N A237998 Number of partitions of 2^n into parts that are at most n.
%H A237998 Alois P. Heinz, <a href="/A237998/b237998.txt">Table of n, a(n) for n = 0..62</a>
%H A237998 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 A237998 a(n) = [x^(2^n)] Product_{j=1..n} 1/(1-x^j).
%F A237998 a(n) ~ 2^(n*(n-1)) / (n!*(n-1)!). - _Vaclav Kotesovec_, Jun 05 2015
%e A237998 a(1) = 1: 11.
%e A237998 a(2) = 3: 22, 211, 1111.
%e A237998 a(3) = 10: 332, 2222, 3221, 3311, 22211, 32111, 221111, 311111, 2111111, 11111111.
%t A237998 a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, 2^n}];
%t A237998 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Nov 03 2018 *)
%Y A237998 Column k=2 of A238010.
%Y A237998 Cf. A236810, A237512, A237999, A238000, A238001, A258672.
%K A237998 nonn
%O A237998 0,3
%A A237998 _Alois P. Heinz_, Feb 16 2014