A013517 - OEIS

A013517

Denominator of [x^(2n+1)] in the Taylor expansion sin(cosec(x)-cot(x))= x/2 + x^3/48 - x^5/1280 - 55*x^7/129024 - 143*x^9/1769472 + ...

2, 48, 1280, 129024, 1769472, 81749606400, 4637432217600, 3296144130048000, 46620662575398912000, 750318428272302489600, 5639235345120252395520000, 72287478143981475374039040000, 7543041197632849604247552000000, 1461479318123759876522171695104000000, 4746884825265972078944013665697792000000

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OFFSET

0,1

COMMENTS

Numerators are apparently provided by A096664.

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = A096671(n) * 2^(2*n+1). - Sean A. Irvine, Aug 07 2018

EXAMPLE

sin(cosec(x) - cot(x)) = x/(2^1*1!) + x^3/(2^3*3!) - 3*x^5/(2^5*5!) - 275*x^7/(2^7*7!) - 15015*x^9/(2^9*9!) - 968167*x^11/(2^11*11!) + ... (apparently covered by A003706).

PROG

(PARI) x = 'x + O('x^50); v = apply(x->denominator(x), Vec(sin(1/sin(x)-cotan(x)))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Sep 20 2018

CROSSREFS

Cf. A096664, A096671.

Sequence in context: A012803 A135394 A010046 * A027509 A348322 A186284

Adjacent sequences: A013514 A013515 A013516 * A013518 A013519 A013520

KEYWORD

nonn,frac

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

EXTENSIONS

Corrected by R. J. Mathar, Dec 18 2011

More terms from Michel Marcus, Sep 20 2018

STATUS

approved