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A233395
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E.g.f.: Sum_{n>=0} ( Sum_{k=1..n} x^k/k )^n / n!.
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1
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1, 1, 1, 4, 10, 46, 236, 1422, 8856, 68868, 592164, 5421384, 54606168, 599176800, 7035165528, 89675702976, 1220188038816, 17545121203296, 266689148404032, 4300256707369056, 73151041156483104, 1307045473317495360, 24472776142475956800, 479965450319937538560, 9829149455867331588480
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OFFSET
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0,4
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COMMENTS
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Compare to: 1/(1-x) = Sum_{n>=0} ( Sum_{k>=1} x^k/k )^n / n!.
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LINKS
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EXAMPLE
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E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 10*x^4/4! + 46*x^5/5! + 236*x^6/6! +...
where
A(x) = 1 + x + (x + x^2/2)^2/2! + (x + x^2/2 + x^3/3)^3/3! + (x + x^2/2 + x^3/3 + x^4/4)^4/4! + (x + x^2/2 + x^3/3 + x^4/4 + x^5/5)^5/5! +...
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PROG
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(PARI) {a(n)=n!*polcoeff(sum(m=0, n, sum(k=1, m, x^k/k +x*O(x^n))^m/m!), n)}
for(n=0, 30, print1(a(n), ", "))
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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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