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Search: id:A157316
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| A157316 |
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G.f.: A(x) = tanh( Sum_{n>=0} 2^((2n+1)^2) * x^(2n+1)/(2n+1) ), with zero terms omitted. |
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1
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| 2, 168, 6710208, 80421395017344, 268650181814894062310400, 241677817414364648836194235222953984, 57560679870262286682598360350282651217048664506368
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OFFSET
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0,1
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COMMENT
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Compare g.f. to the expansion of the inverse tanh of x:
atanh(x) = log((1+x)/(1-x))/2 = x + x^3/3 + x^5/5 + x^7/7 +...
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EXAMPLE
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G.f.: A(x) = 2*x + 168*x^3 + 6710208*x^5 + 80421395017344*x^7 +...
atanh(A(x)) = 2*x + 2^9*x^3/3 + 2^25*x^5/5 + 2^49/7*x^7 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(tanh(sum(m=0, n, 2^((2*m+1)^2)*x^(2*m+1)/(2*m+1))+O(x^(2*n+2))), 2*n+1)}
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CROSSREFS
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Cf. A157315.
Adjacent sequences: A157313 A157314 A157315 this_sequence A157317 A157318 A157319
Sequence in context: A139928 A142602 A005020 this_sequence A163970 A007760 A051030
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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), Mar 19 2009
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