A061079 Denominators in the series for sin integral Si(x).

1, 18, 600, 35280, 3265920, 439084800, 80951270400, 19615115520000, 6046686277632000, 2311256907767808000, 1072909785605898240000, 594596384994354462720000, 387780251083274649600000000, 293999475161295508340736000000, 256411097818451356681764864000000

Offset: 1

Author

Frank Ellermann, May 29 2001

Keywords

• easy
• nonn

Comments

Si(x) = Integral_{t=0..x} sin(t)/t dt.

Examples

			Si(x) = x/1 - x^3/18 + x^5/600 - x^7/35280 + x^9/3265920 -+ ...
		

References

• Bronstein-Semendjajew, Taschenbuch der Mathematik, 13th ed. 1974, ch. 4.3.7, integral 283 of 515.
• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 38, equation 38:6:1 at page 364.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
• Eric Weisstein's World of Mathematics, Shi.

Programs

Magma

[(2*n-1)*Factorial(2*n-1): n in [1..20]]; // Vincenzo Librandi, Dec 01 2011

Mathematica

Table[(2n-1)*(2n-1)!,{n,1,20}] (* Vincenzo Librandi, Dec 01 2011 *)

Formula

a(n) = (2n-1)*(2n-1)!.

From Sergei N. Gladkovskii, Nov 29 2011: (Start)

E.g.f.: A(x) = Si(x) = x + x^3/(W(0) - x^2);

W(k) = x^2*(2*k+1) - (2*k+2)*(2*k+3)^2 + 2*x^2*(k+1)*(2*k+3)^3/W(k+1); (continued fraction).

E.g.f.: A(x) = Si(x) = x - x^3/18 + x^5/(12*W(0) + 18*(x^2) + 324);

W(k) = 16*k^3 + 68*k^2 + 84*k + 23 - x^2*(2*k+1)*(2*k+3)/(2+(2*k+4)*(2*k+5)^3/W(k+1)); (continued fraction).

E.g.f.: A(x) = Si(x) = x*W(0);

W(k) = 1 - x^2*(4*k+1)/((4*k+2)*(4*k+3)^2 - x^2*(4*k+2)*(4*k+3)^3/((4*k+3)*x^2 - (4*k+4)*(4*k+5)^2/W(k+1))); (continued fraction). (End)