OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..434 (terms 0..200 from Vaclav Kotesovec)
FORMULA
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
EXAMPLE
E.g.f. = 1 - 12*x^4/4! + 120*x^5/5! - 1020*x^6/6! + ...
MAPLE
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
MATHEMATICA
CoefficientList[Series[Sech[Log[1+x]^2], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Dec 10 2015 *)
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
STATUS
approved