A009013 Expansion of E.g.f.: 1/(cosh(x)*cos(x)) (only powers that are multiples of 4).

1, 4, 1104, 2154304, 15456463104, 295213107733504, 12366226074019221504, 998143138923599406383104, 141496025961835234723147874304, 32857017298796399667445911477551104, 11837460622615877064781409516336792469504

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..121

Programs

Maple

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

Mathematica

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 *)

PARI

N = 4*66;  x = 'x + O('x^N);
egf = 1/(cosh(x)*cos(x));
v = Vec( serlaplace(egf) );
vector(#v\4, n, v[4*n-3])
/* Joerg Arndt, Mar 31 2013 */

Formula

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

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

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

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.