The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A156134

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A156134

Q_2n(sqrt(2)) (see A104035).
(history; published version)

#15 by Susanna Cuyler at Fri Mar 30 08:13:15 EDT 2018

STATUS

proposed

approved

#14 by G. C. Greubel at Fri Mar 30 00:20:15 EDT 2018

STATUS

editing

proposed

#13 by G. C. Greubel at Fri Mar 30 00:20:11 EDT 2018

LINKS

G. C. Greubel, <a href="/A156134/b156134.txt">Table of n, a(n) for n = 0..207</a>

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 *)

PROG

(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

STATUS

approved

editing

#12 by N. J. A. Sloane at Tue Feb 07 03:59:56 EST 2017

STATUS

proposed

approved

#11 by Bruno Berselli at Tue Feb 07 02:45:38 EST 2017

STATUS

editing

proposed

#10 by Bruno Berselli at Tue Feb 07 02:45:24 EST 2017

FORMULA

G.f. cos(x)/(1 - 3*sin(x)^2) = 1 + 5*x^2/2! + 157*x^4/4! + 12425*x^6/6! + .... For other sequences with a g.f. of the form cos(x)/(1 - k*sin^2(x)) see A012494 (k = -1), A001209 (k = 1/2), A000364(k = 1), A000281 (k = 2), and A002437 (k = 4). - Peter Bala, Feb 06 2017

CROSSREFS

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).

STATUS

proposed

editing

#9 by Michel Marcus at Mon Feb 06 13:39:46 EST 2017

STATUS

editing

proposed

#8 by Michel Marcus at Mon Feb 06 13:39:40 EST 2017

MAPLE

# - __Peter Bala_, Feb 06 2017

STATUS

proposed

editing

#7 by Peter Bala at Mon Feb 06 12:37:34 EST 2017

STATUS

editing

proposed

Discussion

Mon Feb 06

13:00

Peter Luschny: We do not need gfun for such a simple thing. And this is really clumsy: "seq(op(2*i-1, L)*(2*i-2)!, i = 1..floor((1/2)*nops(L)));"  What about this:
cos(x)/(1-3*sin(x)^2): series(%, x, 30):  seq(n!*coeff(%, x, n), n=0..29,2);

#6 by Peter Bala at Mon Feb 06 12:37:15 EST 2017

MAPLE

seq(op(2*i-1, L)*(2*i-2)!, i = 1..floor((1/2)*nops(lL)));