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A046979 Denominators of Taylor series for exp(x)*sin(x).

%I A046979 #25 Feb 10 2025 03:14:35
%S A046979 1,1,1,3,1,30,90,630,1,22680,113400,1247400,1,97297200,681080400,
%T A046979 10216206000,1,1389404016000,12504636144000,237588086736000,1,
%U A046979 49893498214560000,548828480360160000,12623055048283680000,1,3786916514485104000000,49229914688306352000000
%N A046979 Denominators of Taylor series for exp(x)*sin(x).
%D A046979 G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
%H A046979 T. D. Noe, <a href="/A046979/b046979.txt">Table of n, a(n) for n=0..100</a>
%H A046979 Herbert S. Wilf, <a href="https://www2.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</a>, Academic Press, NY, 1994. See p. 54.
%F A046979 a(4n) = 1, a(n) = n!/2^floor(n/2).
%e A046979 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 A046979 a:= n-> denom(coeff(series(sin(x)/exp(x), x, n+1), x, n)):
%p A046979 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 17 2017
%t A046979 Denominator[CoefficientList[Series[Exp[x]Sin[x],{x,0,30}],x] ] (* _Harvey P. Dale_, Feb 14 2015 *)
%o A046979 (PARI) a(n) = if (n % 4, n!/2^floor(n/2), 1); \\ _Michel Marcus_, Oct 12 2015
%Y A046979 Cf. A046978, A046981, A052277, A007019, A007452, A009775, A092820.
%Y A046979 Essentially the same as absolute values of A007415.
%K A046979 nonn,frac,easy,nice
%O A046979 0,4
%A A046979 _N. J. A. Sloane_