A009013 - OEIS

%I #29 Jul 21 2018 23:38:11

%S 1,4,1104,2154304,15456463104,295213107733504,12366226074019221504,

%T 998143138923599406383104,141496025961835234723147874304,

%U 32857017298796399667445911477551104,11837460622615877064781409516336792469504

%N Expansion of E.g.f.: 1/(cosh(x)*cos(x)) (only powers that are multiples of 4).

%H G. C. Greubel, <a href="/A009013/b009013.txt">Table of n, a(n) for n = 0..121</a>

%F E.g.f.: 1/( cos(x)* cosh(x) ) (omitting zero terms).

%F E.g.f.: 1+(x^4)/Q(0); Q(k)=2*(8*k+1)*(16*k^2+4*k+3)-(x^4)/(1+(4*k+1)*(4*k+2)*(4*k+3)*(k+1)/Q(k+1)); (continued fraction). - _Sergei N. Gladkovskii_, Nov 22 2011

%F E.g.f.: 1 - 1/(2*E(0) - 1), where E(k) =  1 - (2*k+1)*(4*k+1)/(x^2 - x^2/(1 - 1/(1 - (2*k+2)*(4*k+3)/(x^2 + x^2/(1 - 1/E(k+1) ))))); (continued fraction). - _Sergei N. Gladkovskii_, Mar 30 2013

%p seq(coeff(series(factorial(n)*(1/(cosh(x)*cos(x))), x,n+1),x,n),n=0..50,4); # _Muniru A Asiru_, Jul 21 2018

%t With[{nmax = 100}, CoefficientList[Series[1/(Cos[x]*Cosh[x]), {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 4]] (* _G. C. Greubel_, Jul 21 2018 *)

%o (PARI)

%o N = 4*66;  x = 'x + O('x^N);

%o egf = 1/(cosh(x)*cos(x));

%o v = Vec( serlaplace(egf) );

%o vector(#v\4, n, v[4*n-3])

%o /* _Joerg Arndt_, Mar 31 2013 */

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested Mar 15 1997 by _Olivier Gérard_.