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A229227 The partition function G(n,10).

%I A229227 #10 May 21 2018 15:23:59
%S A229227 1,1,2,5,15,52,203,877,4140,21147,115975,678569,4213584,27644267,
%T A229227 190897305,1382935569,10479884654,82861996310,682044632178,
%U A229227 5832378929502,51720008131148,474821737584174,4506150050048604,44145239041717738,445876518513670356
%N A229227 The partition function G(n,10).
%C A229227 Number G(n,10) of set partitions of {1,...,n} into sets of size at most 10.
%H A229227 Alois P. Heinz, <a href="/A229227/b229227.txt">Table of n, a(n) for n = 0..500</a>
%F A229227 E.g.f.: exp(Sum_{j=1..10} x^j/j!).
%p A229227 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229227       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229227       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229227     end:
%p A229227 a:= n-> G(n, 10):
%p A229227 seq(a(n), n=0..30);
%p A229227 # second Maple program:
%p A229227 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A229227        a(n-i)*binomial(n-1, i-1), i=1..min(n, 10)))
%p A229227     end:
%p A229227 seq(a(n), n=0..30);  # _Alois P. Heinz_, Sep 22 2016
%t A229227 CoefficientList[Exp[Sum[x^j/j!, {j, 1, 10}]] + O[x]^25, x]*Range[0, 24]! (* _Jean-François Alcover_, May 21 2018 *)
%Y A229227 Column k=10 of A229223.
%Y A229227 Cf. A276930.
%K A229227 nonn
%O A229227 0,3
%A A229227 _Alois P. Heinz_, Sep 16 2013