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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 + ...
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%I #18 Aug 07 2018 20:21:21

%S 1,2,8,16,128,3840,15360,92160,1474560,185794560,3715891200,117964800,

%T 2831155200,51011754393600,13603134504960,8569974738124800,

%U 1371195958099968000,46620662575398912000,239763407530622976000

%N 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 + ...

%C The numerators are apparently the same as A047691.

%F a(n) = A047692(n) * 2^n. - _Sean A. Irvine_, Aug 07 2018

%e 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!)+ ...

%p A013516 := proc(n)

%p exp(csc(x)-cot(x)) ;

%p coeftayl( %,x=0,n) ;

%p denom(%) ;

%p end proc: # _R. J. Mathar_, Dec 18 2011

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

%K nonn,frac

%O 0,2

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

%E Corrected by _R. J. Mathar_, Dec 18 2011