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A141369 E.g.f. satisfies: A(x) = exp(x*A(-x)). +0
2
1, 1, -1, -8, 21, 336, -1445, -35328, 212009, 7010560, -54073449, -2258780160, 21303275389, 1076400869376, -12005345614093, -712084337721344, 9169911825026385, 624667885401341952, -9122376282532978769, -701910552416102645760, 11462725659070874233061 (list; graph; listen)
OFFSET

0,4

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]

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! -++-...

PROGRAM

(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]

CROSSREFS

Cf. A096538.

Sequence in context: A054855 A100903 A156239 this_sequence A060390 A019281 A013630

Adjacent sequences: A141366 A141367 A141368 this_sequence A141370 A141371 A141372

KEYWORD

sign

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 28 2008

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Last modified December 7 08:40 EST 2009. Contains 170430 sequences.


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