%I
%S 1,2,6,70,18886,3534626502,313999279896461576406,
%T 6253297416830848418609522661421870085933646
%N a(n+1) = Product from k=0 to k=n of 1 + C(n,k)*a(k), with a(0) = 1 and C(n,k) the ordinary binomial coefficient.
%C A product analog of the Bell numbers.
%D H. W. Gould, A product analog of the Bell numbers, unpublished manuscript, Jun 03 2007.
%e a(5) = (1+1)(1+8)(1+36)(1+280)(1+18886)
%p A129785 := proc(n)
%p a := 1 ;
%p for k from 0 to n1 do
%p a := a*(1+binomial(n1,k)*procname(k)) ;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Nov 24 2013
%t Clear[a]; a[n_]:= a[n] = Product[1 + Binomial[n1, k]*a[k], {k, 0, n1}]; a[0] = 1; Table[a[n], {n, 0, 10}] (* _Vaclav Kotesovec_, Oct 27 2017 *)
%K easy,nonn
%O 0,2
%A _Henry Gould_, Jun 03 2007
