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Search: id:A095883
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| A095883 |
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Let F(x) be the function such that F(F(x)) = arcsin(x), then F(x) = Sum_{n>=0} a(n)/2^n*x^(2n+1)/(2n+1)!. |
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+0
3
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| 1, 1, 13, 501, 38617, 4945385, 944469221, 250727790173, 88106527550129, 39555449833828817, 22093952731139969213, 15041143328788464370373, 12273562321018687866908553, 11833097802606125967312406457
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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It appears that there are no negative terms.
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EXAMPLE
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F(x) =
x+1/2*x^3/3!+13/2^2*x^5/5!+501/2^3*x^7/7!+38617/2^4*x^9/9!+...
Special values:
F(x)=Pi/6 at x=F(1/2) = 0.51137532057552418592144885355...
F(x)=Pi/4 at x=F(sqrt(2)/2) = 0.74287348600976...
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PROGRAM
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(PARI) {a(n)=local(A, B, F); F=asin(x+x*O(x^(2*n+1))); A=F; for(i=0, n, B=serreverse(A); A=(A+subst(B, x, F))/2); 2^n*(2*n+1)!*polcoeff(A, 2 *n+1, x)}
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CROSSREFS
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Cf. A095882, A095884, A095885.
Sequence in context: A012143 A055412 A116114 this_sequence A139168 A030256 A023332
Adjacent sequences: A095880 A095881 A095882 this_sequence A095884 A095885 A095886
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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 10 2004
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