cp's OEIS Frontend

A057837 Number of partitions of a set of n elements where the partitions are of size > 3.

%I A057837 #41 Jul 02 2025 16:02:00
%S A057837 1,0,0,0,1,1,1,1,36,127,337,793,7525,48764,238954,997790,6401435,
%T A057837 49107697,345482807,2150694855,14656830110,116678887407,978172378669,
%U A057837 7886661080873,63905475745765,553437891603452,5122279358273976,48331088541366296,458771027309344261
%N A057837 Number of partitions of a set of n elements where the partitions are of size > 3.
%H A057837 Seiichi Manyama, <a href="/A057837/b057837.txt">Table of n, a(n) for n = 0..583</a> (terms 0..250 from Alois P. Heinz)
%H A057837 E. A. Enneking and J. C. Ahuja, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/14-1/enneking.pdf">Generalized Bell numbers</a>, Fib. Quart., 14 (1976), 67-73.
%H A057837 I. Mezo, <a href="http://arxiv.org/abs/1308.1637">Periodicity of the last digits of some combinatorial sequences</a>, arXiv preprint arXiv:1308.1637 [math.CO], 2013 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Mezo/mezo19.html">J. Int. Seq. 17 (2014) #14.1.1</a>.
%F A057837 E.g.f.: exp(exp(x)-1-x-x^2/2-x^3/6).
%F A057837 a(0) = 1; a(n) = Sum_{k=4..n} binomial(n-1,k-1) * a(n-k). - _Ilya Gutkovskiy_, Feb 09 2020
%p A057837 G:={P=Set(Set(Atom,card>=4))}:combstruct[gfsolve](G,unlabeled,x):seq(combstruct[count]([P,G,labeled],size=i),i=0..26); # _Zerinvary Lajos_, Dec 16 2007
%t A057837 With[{nn=30},CoefficientList[Series[Exp[Exp[x]-1-x-x^2/2-x^3/6],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Jun 28 2012 *)
%Y A057837 Column k=3 of A293024.
%Y A057837 Row sums of A059023.
%Y A057837 Cf. A000110, A000296, A006505, A057814.
%Y A057837 Cf. A293039.
%K A057837 easy,nice,nonn
%O A057837 0,9
%A A057837 Steven C. Fairgrieve (fsteven(AT)math.wvu.edu), Nov 06 2000
%E A057837 Corrected and extended by _Christian G. Bower_ and _James Sellers_, Nov 09 2000