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

0,9

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.

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

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 *)

Crossrefs

Column k=3 of A293024.

Row sums of A059023.

Cf. A000110, A000296, A006505, A057814.

Cf. A293039.

Sequence in context: A238032 A365506 A250625 * A352316 A007265 A260130

Adjacent sequences: A057834 A057835 A057836 * A057838 A057839 A057840

Keyword

easy,nice,nonn

Author

Steven C. Fairgrieve (fsteven(AT)math.wvu.edu), Nov 06 2000

Extensions

Corrected and extended by Christian G. Bower and James A. Sellers, Nov 09 2000

Status

approved