A013516 Denominators in the Taylor expansion exp(cosec(x)-cot(x))=1 + x/2 + x^2/8 + x^3/16 + 3*x^4/128 + 37*x^5/3840 + 59*x^6/15360 + ...

1, 2, 8, 16, 128, 3840, 15360, 92160, 1474560, 185794560, 3715891200, 117964800, 2831155200, 51011754393600, 13603134504960, 8569974738124800, 1371195958099968000, 46620662575398912000, 239763407530622976000

Offset

0,2

Comments

The numerators are apparently the same as A047691.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = A047692(n) * 2^n. - Sean A. Irvine, Aug 07 2018

Example

exp(cosec(x)-cot(x)) = 1 +1*x/(2^1*1!) + 1*x^2/(2^2*2!) + 3*x^3/(2^3*3!) + 9*x^4/(2^4*4!) + 37*x^5/(2^5*5!) +  177*x^6/(2^6*6!) +959*x^7/(2^7*7!)+ ...

Maple

A013516 := proc(n)
        exp(csc(x)-cot(x)) ;
        coeftayl( %, x=0, n) ;
        denom(%) ;
end proc:  # R. J. Mathar, Dec 18 2011

Crossrefs

Cf. A006229, A002425 (expansion of cosec(x)-cot(x)).

Sequence in context: A046161 A092978 A280777 * A259688 A101059 A191999

Adjacent sequences: A013513 A013514 A013515 * A013517 A013518 A013519

Keyword

nonn,frac

Author

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

Extensions

Corrected by R. J. Mathar, Dec 18 2011

Status

approved