A012273 - OEIS

%I #19 Sep 08 2022 08:44:38

%S 1,0,0,0,12,-120,1020,-8820,89628,-1109808,15992160,-253374000,

%T 4306032192,-78317306496,1529483150832,-32072509450800,

%U 719140990648848,-17146103389588608,432647748528869376

%N 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 ...

%H Vaclav Kotesovec, <a href="/A012273/b012273.txt">Table of n, a(n) for n = 0..400</a>

%H Vaclav Kotesovec, <a href="/A012273/a012273.jpg">Graph - abs(e.g.f.) in the complex plane</a>

%F a(n) ~ n! / (sqrt(2*Pi) * (exp(sqrt(Pi/2))-1) * (exp(-sqrt(Pi/2))-1)^n). - _Vaclav Kotesovec_, Feb 08 2015

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

%p 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

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

%o (PARI) x='x+O('x^30); Vec(serlaplace(1/cos(log(x+1)^2))) \\ _G. C. Greubel_, Oct 28 2018

%o (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

%K sign

%O 0,5

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

%E Definition clarified by _Harvey P. Dale_, Sep 13 2014