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

%I A057814 #33 Jan 05 2025 19:51:36
%S A057814 1,0,0,0,0,1,1,1,1,1,127,463,1255,3004,6722,140570,1039260,5371627,
%T A057814 23202077,90048525,814737785,7967774337,62895570839,417560407223,
%U A057814 2455461090505,18440499041402,179627278800426,1770970802250146
%N A057814 Number of partitions of an n-set into blocks of size > 4.
%H A057814 Seiichi Manyama, <a href="/A057814/b057814.txt">Table of n, a(n) for n = 0..589</a> (terms 0..300 from Alois P. Heinz)
%H A057814 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.
%F A057814 E.g.f.: exp(exp(x)-1-x-x^2/2-x^3/6-x^4/24).
%F A057814 a(0) = 1; a(n) = Sum_{k=5..n} binomial(n-1,k-1) * a(n-k). - _Ilya Gutkovskiy_, Feb 09 2020
%p A057814 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
%t A057814 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. *)
%Y A057814 Column k=4 of A293024.
%Y A057814 Row sums of A059024.
%Y A057814 Cf. A000110, A000296, A006505, A057837.
%Y A057814 Cf. A293040.
%K A057814 easy,nice,nonn
%O A057814 0,11
%A A057814 Steven C. Fairgrieve (fsteven(AT)math.wvu.edu), Nov 06 2000