A057837 Number of partitions of a set of n elements where the partitions are of size > 3.
1, 0, 0, 0, 1, 1, 1, 1, 36, 127, 337, 793, 7525, 48764, 238954, 997790, 6401435, 49107697, 345482807, 2150694855, 14656830110, 116678887407, 978172378669, 7886661080873, 63905475745765, 553437891603452, 5122279358273976, 48331088541366296, 458771027309344261
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..583 (terms 0..250 from Alois P. Heinz)
- E. A. Enneking and J. C. Ahuja, Generalized Bell numbers, Fib. Quart., 14 (1976), 67-73.
- I. Mezo, Periodicity of the last digits of some combinatorial sequences, arXiv preprint arXiv:1308.1637 [math.CO], 2013 and J. Int. Seq. 17 (2014) #14.1.1.
Crossrefs
Programs
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Maple
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 -
Mathematica
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 *)
Formula
E.g.f.: exp(exp(x)-1-x-x^2/2-x^3/6).
a(0) = 1; a(n) = Sum_{k=4..n} binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Feb 09 2020
Extensions
Corrected and extended by Christian G. Bower and James Sellers, Nov 09 2000