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Search: id:A144015
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| A144015 |
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E.g.f. A(x) = 1/(1 - sin 4x)^(1/4). |
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+0
1
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| 1, 1, 5, 29, 265, 3001, 42125, 696149, 13296145, 287706481, 6959431445, 186061833869, 5448382252825, 173418192216361, 5961442393047965, 220112963745653189, 8687730877758518305, 365023930617143804641
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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E.g.f. satisfies: A^2/A(-x)^2 = 1/cos(4*x) + tan(4*x).
E.g.f. satisfies: A(x) = exp( Integral A^2/A(-x)^2 dx).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 5*x^2/2! + 29*x^3/3! + 265*x^4/4! + 3001*x^5/5! +...
log(A(x)) = x + 4*x^2/2! + 16*x^3/3! + 128*x^4/4! + 1280*x^5/5! +...
A^2/A(-x)^2 = 1 + 4*x + 16*x^2/2! + 128*x^3/3! +...+ 4^n*A000111(n)*x^n/n! +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=exp(intformal(A^2/subst(A^2, x, -x)))); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A000111, A001586, A007788.
Sequence in context: A000354 A103815 A134752 this_sequence A112799 A020531 A087899
Adjacent sequences: A144012 A144013 A144014 this_sequence A144016 A144017 A144018
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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), Sep 09 2008
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