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A356576
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Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^x.
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1
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1, 0, 2, 0, 24, -55, 630, -2723, 30968, -294327, 3047320, -30255379, 387690732, -5565964391, 77090414492, -1114263777885, 18473122449616, -331776991760303, 6106973926830192, -112710455017397639, 2233663985151902860, -50049383051597936559
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k * A352013(k-1) * binomial(n-1,k-1) * a(n-k).
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^x))
(PARI) a352013(n) = (n-1)!*sumdiv(n, d, (-1)^(n/d+1)/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a352013(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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