A012273 Expansion of e.g.f.: sec(log(x+1)*log(x+1)) = 1 + (12/4!)*x^4 - (120/5!)*x^5 + (1020/6!)*x^6 ...

1, 0, 0, 0, 12, -120, 1020, -8820, 89628, -1109808, 15992160, -253374000, 4306032192, -78317306496, 1529483150832, -32072509450800, 719140990648848, -17146103389588608, 432647748528869376

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Vaclav Kotesovec, Graph - abs(e.g.f.) in the complex plane

Formula

a(n) ~ n! / (sqrt(2*Pi) * (exp(sqrt(Pi/2))-1) * (exp(-sqrt(Pi/2))-1)^n). - Vaclav Kotesovec, Feb 08 2015

Example

E.g.f. = 1 + 12*x^4/4! - 120*x^5/5! + 1020*x^6/6! + ...

Maple

seq(coeff(series(factorial(n)*sec(log(x+1)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 28 2018

Mathematica

With[{nn=20}, CoefficientList[Series[Sec[Log[x+1]^2], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Sep 13 2014 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/cos(log(x+1)^2))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Log(x+1)^2) )); [Factorial(n-1)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 28 2018

Crossrefs

Sequence in context: A012274 A009035 A009140 * A008465 A291391 A115902

Adjacent sequences: A012270 A012271 A012272 * A012274 A012275 A012276

Keyword

sign

Author

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

Extensions

Definition clarified by Harvey P. Dale, Sep 13 2014

Status

approved