A156134 Q_2n(sqrt(2)) (see A104035).

1, 5, 157, 12425, 1836697, 436366445, 152053957237, 73053601590065, 46283414838553777, 37386890114969267285, 37503815980582784378317, 45739346519434253222582105, 66650214918099514832427062857, 114363498315755726948758209518525, 228234739109951323288351261455519397

Offset: 0

Author

N. J. A. Sloane, Nov 06 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..207

Crossrefs

Cf. A012494, A001209, A000364, A000281, A002437.

Cf. other sequences with a g.f. of the form cos(x)/(1 - k*sin^2(x)): A012494 (k=-1), A001209 (k=1/2), A000364(k=1), A000281 (k=2), A002437 (k=4).

Programs

Maple

with(gfun):
series(cos(x)/(1-3*sin(x)^2), x, 30):
L := seriestolist(%):
seq(op(2*i-1,L)*(2*i-2)!, i = 1..floor((1/2)*nops(L)));
# Peter Bala, Feb 06 2017

Mathematica

With[{nmax = 50}, CoefficientList[Series[Cos[x]/(1 - 3*Sin[x]^2), {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 2]] (* G. C. Greubel, Mar 29 2018 *)

PARI

x='x+O('x^50); v=Vec(serlaplace(cos(x)/(1 - 3*sin(x)^2))); vector(#v\2,n,v[2*n-1]) \\ G. C. Greubel, Mar 29 2018

Formula

G.f. cos(x)/(1 - 3*sin(x)^2) = 1 + 5*x^2/2! + 157*x^4/4! + 12425*x^6/6! + ... - Peter Bala, Feb 06 2017