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Search: id:A163971
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| A163971 |
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G.f.: A(x) = sin( Sum_{n>=0} 2^[(2n+1)^2] * [(2n)!/(n!*2^n)]^2 * x^(2n+1)/(2n+1)! ). |
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+0
2
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| 2, 84, 2516412, 25131689308776, 73459034127708442263660, 59475400379433834763260101514326040, 12984879931670595437855043594849682375333268239320
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that x = sin( Sum_{n>=0} [(2n)!/(n!*2^n)]^2 * x^(2n+1)/(2n+1)! ).
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EXAMPLE
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G.f.: A(x) = 2*x + 84*x^3 + 2516412*x^5 + 25131689308776*x^7 +...
asin(x) = x + x^3/3! + 3^2*x^5/5! + 15^2*x^7/7! + 105^2*x^9/9! +...
asin(A(x)) = 2*x + 2^9*x^3/3! + 2^25*3^2*x^5/5! + 2^49*15^2*x^7/7! + 2^81*105^2*x^9/9! +...
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PROGRAM
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(PARI) {a(n)=polcoeff(tanh(sum(k=1, 2*n, 2^((2*k-1)^2)*x^(2*k-1)/(2*k-1)+x*O(x^(2*n)))), 2*n-1)}
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CROSSREFS
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Cf. A155200, A163970, A001818.
Sequence in context: A099373 A157063 A157315 this_sequence A078166 A101578 A041881
Adjacent sequences: A163968 A163969 A163970 this_sequence A163972 A163973 A163974
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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), Aug 14 2009
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