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A352914
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Expansion of e.g.f. exp(Sum_{k>=1} prime(k)*x^k).
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1
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1, 2, 10, 74, 676, 7592, 97024, 1416200, 23015248, 412777952, 8090869984, 171435904928, 3908548404160, 95264270043776, 2470715015425024, 67913132377486208, 1971038886452490496, 60212661838223997440, 1930529043247940342272, 64801071784954698480128
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A033286(k) * a(n-k)/(n-k)!.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
ithprime(j)*j*binomial(n, j)*j!, j=1..n)/n)
end:
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = (n-1)! Sum[k Prime[k] a[n-k]/(n-k)!, {k, 1, n}];
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, prime(k)*x^k))))
(PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, k*prime(k)*a(n-k)/(n-k)!));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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