A129785 a(n) = Product_{k=0..n-1} (1 + binomial(n,k)*a(k)), with a(0) = 1.

1, 2, 6, 70, 18886, 3534626502, 313999279896461576406, 6253297416830848418609522661421870085933646

Offset: 0

Author

Henry Gould, Jun 03 2007

Keywords

• easy
• nonn

Comments

A product analog of the Bell numbers.

Examples

			a(5) = (1+1)*(1+8)*(1+36)*(1+280)*(1+18886) = 3534626502.
		

References

• H. W. Gould, A product analog of the Bell numbers, unpublished manuscript, Jun 03 2007.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..11

Programs

Maple

A129785 := proc(n)
    a := 1 ;
    for k from 0 to n-1 do
        a := a*(1+binomial(n-1,k)*procname(k)) ;
    end do:
    a ;
end proc: # R. J. Mathar, Nov 24 2013

Mathematica

a[n_]:= a[n] = Product[1 + Binomial[n-1, k]*a[k], {k, 0, n-1}];
Table[a[n], {n, 0, 10}] (* Vaclav Kotesovec, Oct 27 2017 *)

PARI

a(n)={my(v=vector(n+1)); for(n=0, #v-1, v[1+n]=prod(k=0, n-1, 1 + binomial(n-1, k)*v[1+k])); v[#v]} \\ Andrew Howroyd, Jan 03 2020