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Search: id:A120010
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| A120010 |
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G.f.: A(x) = (1-sqrt(1-4*x))/2 o x/(1-x) o (x-x^2), a composition of functions involving the Catalan function and its inverse. |
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8
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| 1, 1, 1, 2, 6, 18, 53, 158, 481, 1491, 4688, 14913, 47913, 155261, 506881, 1665643, 5504988, 18287338, 61027991, 204499397, 687808931, 2321177071, 7857504876, 26673769002, 90783820081, 309720079813, 1058984020333, 3628267267358
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The n-th self-composition of A(x) is: (1-sqrt(1-4*x))/2 o x/(1-n*x) o (x-x^2) = (1 - sqrt(1 - 4*(x-x^2)/(1-n*x+n*x^2) ))/2. See A120009 for the transpose of the composition of the same functions.
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FORMULA
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G.f.: A(x) = (1 - sqrt(1 - 4*(x-x^2)/(1-x+x^2) ))/2.
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EXAMPLE
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A(x) = x + x^2 + x^3 + 2*x^4 + 6*x^5 + 18*x^6 + 53*x^7 + 158*x^8 +...
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PROGRAM
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(PARI) {a(n)=polcoeff((1 - sqrt(1 - 4*(x-x^2)/(1-x+x^2+x*O(x^n)) ))/2, n)}
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CROSSREFS
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Cf. A120009 (composition transpose), A000108 (Catalan).
Sequence in context: A052979 A005507 A094864 this_sequence A132790 A072850 A072852
Adjacent sequences: A120007 A120008 A120009 this_sequence A120011 A120012 A120013
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 03 2006
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