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A159476
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E.g.f.: A(x) = exp( Sum_{n>=1} (n-1)!*x^n/n ).
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0
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1, 1, 2, 8, 62, 862, 19492, 656224, 30739676, 1906807004, 151002453464, 14846381034784, 1772922018732328, 252631570039665832, 42329528274029082608, 8237406877267427867648, 1842215469973381977889808
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| 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
| 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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PROG
| (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
| Cf. A158876.
Sequence in context: A086903 A161566 A192516 * A006245 A202751 A191604
Adjacent sequences: A159473 A159474 A159475 * A159477 A159478 A159479
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 15 2009
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