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

%I A061079 #32 Feb 16 2025 08:32:44
%S A061079 1,18,600,35280,3265920,439084800,80951270400,19615115520000,
%T A061079 6046686277632000,2311256907767808000,1072909785605898240000,
%U A061079 594596384994354462720000,387780251083274649600000000,293999475161295508340736000000,256411097818451356681764864000000
%N A061079 Denominators in the series for sin integral Si(x).
%C A061079 Si(x) = Integral_{t=0..x} sin(t)/t dt.
%D A061079 Bronstein-Semendjajew, Taschenbuch der Mathematik, 13th ed. 1974, ch. 4.3.7, integral 283 of 515.
%D A061079 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 38, equation 38:6:1 at page 364.
%H A061079 Vincenzo Librandi, <a href="/A061079/b061079.txt">Table of n, a(n) for n = 1..200</a>
%H A061079 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>.
%H A061079 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Shi.html">Shi</a>.
%F A061079 a(n) = (2n-1)*(2n-1)!.
%F A061079 From _Sergei N. Gladkovskii_, Nov 29 2011: (Start)
%F A061079 E.g.f.: A(x) = Si(x) = x + x^3/(W(0) - x^2);
%F A061079 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).
%F A061079 E.g.f.: A(x) = Si(x) = x - x^3/18 + x^5/(12*W(0) + 18*(x^2) + 324);
%F A061079 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).
%F A061079 E.g.f.: A(x) = Si(x) = x*W(0);
%F A061079 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)
%e A061079 Si(x) = x/1 - x^3/18 + x^5/600 - x^7/35280 + x^9/3265920 -+ ...
%t A061079 Table[(2n-1)*(2n-1)!,{n,1,20}] (* _Vincenzo Librandi_, Dec 01 2011 *)
%o A061079 (Magma) [(2*n-1)*Factorial(2*n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 01 2011
%K A061079 easy,nonn
%O A061079 1,2
%A A061079 _Frank Ellermann_, May 29 2001