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A229224 The partition function G(n,7).

%I A229224 #14 May 21 2018 15:14:21
%S A229224 1,1,2,5,15,52,203,877,4139,21137,115874,677623,4204927,27565188,
%T A229224 190168577,1376119903,10414950785,82230347149,675762947626,
%U A229224 5768465148493,51054457464731,467728049807348,4428770289719931,43281554035140829,436015324638219779
%N A229224 The partition function G(n,7).
%C A229224 Number G(n,7) of set partitions of {1,...,n} into sets of size at most 7.
%H A229224 Alois P. Heinz, <a href="/A229224/b229224.txt">Table of n, a(n) for n = 0..500</a>
%F A229224 E.g.f.: exp(Sum_{j=1..7} x^j/j!).
%p A229224 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229224       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229224       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229224     end:
%p A229224 a:= n-> G(n, 7):
%p A229224 seq(a(n), n=0..30);
%p A229224 # second Maple program:
%p A229224 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A229224        a(n-i)*binomial(n-1, i-1), i=1..min(n, 7)))
%p A229224     end:
%p A229224 seq(a(n), n=0..30);  # _Alois P. Heinz_, Sep 22 2016
%t A229224 CoefficientList[Exp[Sum[x^j/j!, {j, 1, 7}]] + O[x]^25, x]*Range[0, 24]! (* _Jean-François Alcover_, May 21 2018 *)
%Y A229224 Column k=7 of A229223.
%Y A229224 Cf. A276927.
%K A229224 nonn
%O A229224 0,3
%A A229224 _Alois P. Heinz_, Sep 16 2013