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A195415
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E.g.f.: Sum_{n>=1} tanh(n*x)^n = Sum_{n>=1} a(n)*4^(n-1)/n!.
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0
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1, 2, 10, 92, 1351, 28982, 855100, 33214232, 1642999501, 100843185962, 7520379392890, 669760178257172, 70211429619908851, 8558006664633638942, 1200128210993564085880, 191861070874818576596912, 34685967730611200643509401, 7041037426518318365605795922
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..18.
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FORMULA
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E.g.f.: Sum_{n>=1} ( 1 - 2/(1+exp(2*n*x)) )^n = Sum_{n>=1} a(n)*4^(n-1)/n!.
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EXAMPLE
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E.g.f.: A(x) = x + 8*x^2/2! + 160*x^3/3! + 5888*x^4/4! + 345856*x^5/5! +...
or, equivalently,
A(x) = x + 2*4*x^2/2! + 10*4^2*x^3/3! + 92*4^3*x^4/4! + 1351*4^4*x^5/5! +...
where
A(x) = tanh(x) + tanh(2*x)^2 + tanh(3*x)^3 + tanh(4*x)^4 + tanh(5*x)^5 +...
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PROG
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(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=1, n, tanh(m*X)^m); n!/4^(n-1)*polcoeff(Egf, n)}
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CROSSREFS
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Sequence in context: A182952 A108209 A111773 * A181084 A063385 A063393
Adjacent sequences: A195412 A195413 A195414 * A195416 A195417 A195418
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Sep 17 2011
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STATUS
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approved
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