A012274 Expansion of e.g.f.: sech(log(x+1)*log(x+1)).

1, 0, 0, 0, -12, 120, -1020, 8820, -72828, 505008, -1376160, -51546000, 1698674208, -38050144704, 739129595568, -12975913969200, 200099389809552, -2317325113329792, 740464178471424

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

Sequence in context: A061506 A059155 A012443 * A009035 A009140 A012273

Adjacent sequences: A012271 A012272 A012273 * A012275 A012276 A012277

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved