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A009013 Expansion of E.g.f.: 1/(cosh(x)*cos(x)) (only powers that are multiples of 4). 2
1, 4, 1104, 2154304, 15456463104, 295213107733504, 12366226074019221504, 998143138923599406383104, 141496025961835234723147874304, 32857017298796399667445911477551104, 11837460622615877064781409516336792469504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

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 *)

PROG

(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 */

CROSSREFS

Sequence in context: A221228 A159859 A110499 * A351618 A248656 A357512

Adjacent sequences: A009010 A009011 A009012 * A009014 A009015 A009016

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Extended and signs tested Mar 15 1997 by Olivier Gérard.

STATUS

approved

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Last modified February 7 19:43 EST 2023. Contains 360128 sequences. (Running on oeis4.)