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A141369
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E.g.f. satisfies: A(x) = exp(x*A(-x)).
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2
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1, 1, -1, -8, 21, 336, -1445, -35328, 212009, 7010560, -54073449, -2258780160, 21303275389, 1076400869376, -12005345614093, -712084337721344, 9169911825026385, 624667885401341952, -9122376282532978769, -701910552416102645760, 11462725659070874233061
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| E.g.f.: A(x) = exp(x*exp(-x*exp(x*exp(-x*exp(x*...))))).
a(n+1) = Sum_{i=0..n} (i+1)*(-1)^i*binomial(n,i)*a(i)*a(n-i) - from a formula given in A096538 by Vladeta Jovovic (vladeta(AT)eunet.rs).
a(n) = Sum_{k=0..n} (-1)^(n-k) * C(n,k) * (n-k+1)^(k-1) * k^(n-k). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 13 2009]
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EXAMPLE
| E.g.f.: A(x) = 1 + x - x^2/2! - 8*x^3/3! + 21*x^4/4! + 336*x^5/5! --++...
Log(A(x)) = x - x^2 - x^3/2! + 8*x^4/3! + 21*x^4/4! - 336*x^5/5! -++-...
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PROG
| (PARI) {a(n)=local(A=1); for(i=0, n, A=exp((-1)^(n-i)*x*A+x*O(x^n))); n!*polcoeff(A, n)}
(PARI) {a(n)=sum(k=0, n, (-1)^(n-k)*binomial(n, k)*(n-k+1)^(k-1)*k^(n-k))} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 13 2009]
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CROSSREFS
| Cf. A096538.
Sequence in context: A054855 A100903 A156239 * A060390 A019281 A013630
Adjacent sequences: A141366 A141367 A141368 * A141370 A141371 A141372
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 28 2008
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