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

1, 1, 1, 3, 1, 30, 90, 630, 1, 22680, 113400, 1247400, 1, 97297200, 681080400, 10216206000, 1, 1389404016000, 12504636144000, 237588086736000, 1, 49893498214560000, 548828480360160000, 12623055048283680000, 1, 3786916514485104000000, 49229914688306352000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy
• nice

Examples

			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 + ...
		

References

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

Links

• T. D. Noe, Table of n, a(n) for n=0..100
• Herbert S. Wilf, Generatingfunctionology, Academic Press, NY, 1994. See p. 54.

Crossrefs

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

Essentially the same as absolute values of A007415.

Programs

Maple

a:= n-> denom(coeff(series(sin(x)/exp(x), x, n+1), x, n)):
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 17 2017

Mathematica

Denominator[CoefficientList[Series[Exp[x]Sin[x],{x,0,30}],x] ] (* Harvey P. Dale, Feb 14 2015 *)

PARI

a(n) = if (n % 4, n!/2^floor(n/2), 1); \\ Michel Marcus, Oct 12 2015

Formula

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