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A129785 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. 1

%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%D H. W. Gould, A product analog of the Bell numbers, unpublished manuscript, Jun 03 2007.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 n-1 do

%p a := a*(1+binomial(n-1,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[n-1, k]*a[k], {k, 0, n-1}]; 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

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Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)