cp's OEIS Frontend

A229225 The partition function G(n,8).

%I A229225 #10 May 21 2018 15:23:33
%S A229225 1,1,2,5,15,52,203,877,4140,21146,115964,678448,4212352,27632112,
%T A229225 190778186,1381763398,10468226150,82744297014,680835331228,
%U A229225 5819712427654,51584619782546,473344099095848,4489677962922186,43957668431564086,443694809361207824
%N A229225 The partition function G(n,8).
%C A229225 Number G(n,8) of set partitions of {1,...,n} into sets of size at most 8.
%H A229225 Alois P. Heinz, <a href="/A229225/b229225.txt">Table of n, a(n) for n = 0..500</a>
%F A229225 E.g.f.: exp(Sum_{j=1..8} x^j/j!).
%p A229225 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229225       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229225       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229225     end:
%p A229225 a:= n-> G(n, 8):
%p A229225 seq(a(n), n=0..30);
%p A229225 # second Maple program:
%p A229225 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A229225        a(n-i)*binomial(n-1, i-1), i=1..min(n, 8)))
%p A229225     end:
%p A229225 seq(a(n), n=0..30);  # _Alois P. Heinz_, Sep 22 2016
%t A229225 CoefficientList[Exp[Sum[x^j/j!, {j, 1, 8}]] + O[x]^25, x]*Range[0, 24]! (* _Jean-François Alcover_, May 21 2018 *)
%Y A229225 Column k=8 of A229223.
%Y A229225 Cf. A276928.
%K A229225 nonn
%O A229225 0,3
%A A229225 _Alois P. Heinz_, Sep 16 2013