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Denominators of Taylor series for exp(x)*sin(x).
7

%I #21 Nov 17 2017 19:38:58

%S 1,1,1,3,1,30,90,630,1,22680,113400,1247400,1,97297200,681080400,

%T 10216206000,1,1389404016000,12504636144000,237588086736000,1,

%U 49893498214560000,548828480360160000,12623055048283680000,1,3786916514485104000000,49229914688306352000000

%N Denominators of Taylor series for exp(x)*sin(x).

%D G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.

%H T. D. Noe, <a href="/A046979/b046979.txt">Table of n, a(n) for n=0..100</a>

%F a(4n) = 1, a(n) = n!/2^floor(n/2).

%e 1*x + 1*x^2 + 1/3*x^3 - 1/30*x^5 - 1/90*x^6 - 1/630*x^7 + 1/22680*x^9 + 1/113400*x^10 + ...

%p a:= n-> denom(coeff(series(sin(x)/exp(x), x, n+1), x, n)):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Nov 17 2017

%t Denominator[CoefficientList[Series[Exp[x]Sin[x],{x,0,30}],x] ] (* _Harvey P. Dale_, Feb 14 2015 *)

%o (PARI) a(n) = if (n % 4, n!/2^floor(n/2), 1); \\ _Michel Marcus_, Oct 12 2015

%Y Cf. A046978, A046981, A052277, A007019, A007452, A009775, A092820.

%Y Essentially the same as absolute values of A007415.

%K nonn,frac,easy,nice

%O 0,4

%A _N. J. A. Sloane_