A057814 Number of partitions of an n-set into blocks of size > 4.

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 127, 463, 1255, 3004, 6722, 140570, 1039260, 5371627, 23202077, 90048525, 814737785, 7967774337, 62895570839, 417560407223, 2455461090505, 18440499041402, 179627278800426, 1770970802250146

Offset: 0

Author

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

Keywords

• easy
• nice
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..589 (terms 0..300 from Alois P. Heinz)
• E. A. Enneking and J. C. Ahuja, Generalized Bell numbers, Fib. Quart., 14 (1976), 67-73.

Crossrefs

Column k=4 of A293024.

Row sums of A059024.

Cf. A000110, A000296, A006505, A057837.

Cf. A293040.

Programs

Maple

G:={P=Set(Set(Atom,card>=5))}:combstruct[gfsolve](G,labeled,x):seq(combstruct[count]([P,G,labeled],size=i),i=0..27); # Zerinvary Lajos, Dec 16 2007

Mathematica

max = 27; CoefficientList[ Series[ Exp[ Exp[x] - Normal[ Series[ Exp[x], {x, 0, 4}]]], {x, 0, max}], x]*Range[0, max]!(* Jean-François Alcover, Apr 25 2012, from e.g.f. *)

Formula

E.g.f.: exp(exp(x)-1-x-x^2/2-x^3/6-x^4/24).

a(0) = 1; a(n) = Sum_{k=5..n} binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Feb 09 2020