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A129785
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a(n) = Product_{k=0..n-1} (1 + binomial(n,k)*a(k)), with a(0) = 1.
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1
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OFFSET
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0,2
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COMMENTS
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A product analog of the Bell numbers.
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REFERENCES
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H. W. Gould, A product analog of the Bell numbers, unpublished manuscript, Jun 03 2007.
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LINKS
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EXAMPLE
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a(5) = (1+1)*(1+8)*(1+36)*(1+280)*(1+18886) = 3534626502.
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MAPLE
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a := 1 ;
for k from 0 to n-1 do
a := a*(1+binomial(n-1, k)*procname(k)) ;
end do:
a ;
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MATHEMATICA
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a[n_]:= a[n] = Product[1 + Binomial[n-1, k]*a[k], {k, 0, n-1}];
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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