A229227 - OEIS

%I #10 May 21 2018 15:23:59

%S 1,1,2,5,15,52,203,877,4140,21147,115975,678569,4213584,27644267,

%T 190897305,1382935569,10479884654,82861996310,682044632178,

%U 5832378929502,51720008131148,474821737584174,4506150050048604,44145239041717738,445876518513670356

%N The partition function G(n,10).

%C Number G(n,10) of set partitions of {1,...,n} into sets of size at most 10.

%H Alois P. Heinz, <a href="/A229227/b229227.txt">Table of n, a(n) for n = 0..500</a>

%F E.g.f.: exp(Sum_{j=1..10} x^j/j!).

%p G:= proc(n, k) option remember; local j; if k>n then G(n, n)

%p       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);

%p       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi

%p     end:

%p a:= n-> G(n, 10):

%p seq(a(n), n=0..30);

%p # second Maple program:

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p        a(n-i)*binomial(n-1, i-1), i=1..min(n, 10)))

%p     end:

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Sep 22 2016

%t CoefficientList[Exp[Sum[x^j/j!, {j, 1, 10}]] + O[x]^25, x]*Range[0, 24]! (* _Jean-François Alcover_, May 21 2018 *)

%Y Column k=10 of A229223.

%Y Cf. A276930.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 16 2013