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Search: id:A157674
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| A157674 |
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G.f.: A(x) = 1 + x/exp( Sum_{k>=1} [A((-1)^k*x) - 1]^k/k ). |
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+0
2
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| 1, 1, 1, -1, -3, 1, 9, 1, -27, -13, 81, 67, -243, -285, 729, 1119, -2187, -4215, 6561, 15505, -19683, -56239, 59049, 202309, -177147, -724499, 531441, 2589521, -1594323, -9254363, 4782969, 33111969, -14348907, -118725597, 43046721
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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G.f.: A(x) = sqrt(1+4*x^2)/(sqrt(1+4*x^2) - x).
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 - x^3 - 3*x^4 + x^5 + 9*x^6 + x^7 - 27*x^8 -...
ILLUSTRATION OF G.F.:
A(x) = 1 + x/exp([A(-x)-1] + [A(x)-1]^2/2 + [A(-x)-1]^3/3 + [A(x)-1]^4/4 +...)
RELATED EXPANSION:
Coefficients of 1/A(x) include central binomial coefficients:
[1, -1, 0, 2, 0, -6, 0, 20, 0, -70, 0, 252, 0, -924,...].
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*exp(-sum(k=1, n, (subst(A, x, (-1)^k*x+x*O(x^n))-1)^k/k))); polcoeff(A, n)}
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CROSSREFS
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Cf. A000984, A156909.
Sequence in context: A070894 A090261 A130599 this_sequence A063467 A021762 A019736
Adjacent sequences: A157671 A157672 A157673 this_sequence A157675 A157676 A157677
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2009
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