cp's OEIS Frontend

A229226 The partition function G(n,9).

%I A229226 #10 May 21 2018 15:23:47
%S A229226 1,1,2,5,15,52,203,877,4140,21147,115974,678558,4213452,27642837,
%T A229226 190882290,1382779413,10478259030,82844940414,681863474058,
%U A229226 5830425411936,51698581146426,474582397380708,4503425395487976,44113612993755306,445502134752984696
%N A229226 The partition function G(n,9).
%C A229226 Number G(n,9) of set partitions of {1,...,n} into sets of size at most 9.
%H A229226 Alois P. Heinz, <a href="/A229226/b229226.txt">Table of n, a(n) for n = 0..500</a>
%F A229226 E.g.f.: exp(Sum_{j=1..9} x^j/j!).
%p A229226 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229226       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229226       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229226     end:
%p A229226 a:= n-> G(n, 9):
%p A229226 seq(a(n), n=0..30);
%p A229226 # second Maple program:
%p A229226 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A229226        a(n-i)*binomial(n-1, i-1), i=1..min(n, 9)))
%p A229226     end:
%p A229226 seq(a(n), n=0..30);  # _Alois P. Heinz_, Sep 22 2016
%t A229226 CoefficientList[Exp[Sum[x^j/j!, {j, 1, 9}]] + O[x]^25, x]*Range[0, 24]! (* _Jean-François Alcover_, May 21 2018 *)
%Y A229226 Column k=9 of A229223.
%Y A229226 Cf. A276929.
%K A229226 nonn
%O A229226 0,3
%A A229226 _Alois P. Heinz_, Sep 16 2013