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A012274
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Expansion of e.g.f.: sech(log(x+1)*log(x+1)).
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1
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1, 0, 0, 0, -12, 120, -1020, 8820, -72828, 505008, -1376160, -51546000, 1698674208, -38050144704, 739129595568, -12975913969200, 200099389809552, -2317325113329792, 740464178471424
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OFFSET
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0,5
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LINKS
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FORMULA
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Lim sup n->infinity |a(n)/n!|^(1/n) = exp(sqrt(Pi)/4) / sqrt(2*(cosh(sqrt(Pi)/2) - cos(sqrt(Pi)/2))) = 1.24168087005499040594... . - Vaclav Kotesovec, Dec 10 2015
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EXAMPLE
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E.g.f. = 1 - 12*x^4/4! + 120*x^5/5! - 1020*x^6/6! + ...
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MAPLE
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seq(coeff(series(factorial(n)*sech(log(x+1)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 28 2018
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MATHEMATICA
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CoefficientList[Series[Sech[Log[1+x]^2], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Dec 10 2015 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(1/cosh(log(x+1)^2))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cosh(Log(x+1)^2) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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