A007415 Expand sin x / exp x = x-x^2+x^3/3-x^5/30+... and invert nonzero coefficients.

0, 1, -1, 3, 0, -30, 90, -630, 0, 22680, -113400, 1247400, 0, -97297200, 681080400, -10216206000, 0, 1389404016000, -12504636144000, 237588086736000, 0, -49893498214560000, 548828480360160000, -12623055048283680000, 0, 3786916514485104000000

Offset

0,4

Links

Table of n, a(n) for n=0..25.

J. Roberts, Lure of the Integers, Annotated scanned copy of pp. 81, 86 with notes.

Formula

a(n) = [n mod 4 > 0] * (-1)^(n+1+[n/4]) * n!/2^[n/2]. - Ralf Stephan, Mar 06 2004

E.g.f.: sin(x)/exp(x) = x-x^2/(G(0)+x); G(k)=2k+1-x+x*(2k+1)/(4k+3-x+x^2*(4k+3)/( (2k+2)*(4k+5)-x^2+x*(2k+2)*(4k+5)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 20 2011

Maple

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

Mathematica

1/CoefficientList[Sin[x]/Exp[x] + O[x]^26, x] /. ComplexInfinity -> 0 // Quiet (* Jean-François Alcover, Feb 26 2019 *)

Crossrefs

Absolute values are essentially the same as A046979, where zeros are replaced by ones.

a(4n+2) = -(-1)^n*A052277(n), a(2n+1) = (-1)^[n/2]*A007019(n).

Cf. A046981, A007452, A009775, A092820.

Sequence in context: A215683 A215586 A215680 * A145222 A058833 A368284

Adjacent sequences: A007412 A007413 A007414 * A007416 A007417 A007418

Keyword

sign

Author

N. J. A. Sloane.

Status

approved