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A159476
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Expansion of e.g.f.: A(x) = exp( Sum_{n>=1} (n-1)!*x^n/n ).
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2
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1, 1, 2, 8, 62, 862, 19492, 656224, 30739676, 1906807004, 151002453464, 14846381034784, 1772922018732328, 252631570039665832, 42329528274029082608, 8237406877267427867648, 1842215469973381977889808, 469160036709398319115207696, 134976328490030629922214893344
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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(n) = (n-1)!*Sum_{k=1..n} (k-1)!*a(n-k)/(n-k)! for n > 0 with a(0)=1.
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 62*x^4/4! + 862*x^5/5! + ...
log(A(x)) = x + x^2/2 + 2!*x^3/3 + 3!*x^4/4 + 4!*x^5/5 + 5!*x^6/6 + ...
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-i)*binomial(n-1, i-1)*(i-1)!^2, i=1..n))
end:
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MATHEMATICA
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a:= CoefficientList[Series[Exp[Sum[(n - 1)!*x^n/n, {n, 1, 500}]], {x, 0, 35}], x]; Table[a[[n]]*(n - 1)!, {n, 1, 30}] (* G. C. Greubel, Jul 09 2018 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(exp(sum(k=1, n, (k-1)!*x^k/k)+x*O(x^n)), n)}
(PARI) {a(n)=if(n==0, 1, (n-1)!*sum(k=1, n, (k-1)!*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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