# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a126119 Showing 1-1 of 1 %I A126119 #17 Mar 01 2014 05:00:56 %S A126119 1,5,27,195,1785,19845,259875,3918915,66891825,1274998725,26843892075, %T A126119 618718975875,15495473018025,419010239773125,12167108660581875, %U A126119 377607284571391875,12473420957563190625,436953531082636693125,16179945969799083346875,631461179013117650071875 %N A126119 Numerators of sequence of fractions with e.g.f. (1+x)/(1-x)^(3/2). %C A126119 Denominators are successive powers of 2. %H A126119 Vincenzo Librandi, Table of n, a(n) for n = 0..200 %F A126119 E.g.f.: (1+2*x)/(1-2*x)^(3/2) %F A126119 From _Sergei N. Gladkovskii_, Jul 23 2012: (Start) %F A126119 a(n) = (4*n+1)*((2*n)!)/( n!*(2^n) ). %F A126119 G.f.: 3*Q(0), where Q(k)= 1 - (2*k+2)/(3*(2*k+1) - 9*x*(2*k+1)^2*(2*k+3)/(3*x*(2*k+1)*(2*k+3) - (2*k+2)/Q(k+1))); (continued fraction, 3rd kind, 3-step). %F A126119 (End). %F A126119 a(n) ~ 2^(n+5/2) * n^(n+1) / exp(n). - _Vaclav Kotesovec_, Feb 25 2014 %e A126119 The fractions are 1, 5/2, 27/4, 195/8, 1785/16, 19845/32, 259875/64, ... %t A126119 CoefficientList[Series[(1+2*x)/(1-2*x)^(3/2), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 25 2014 *) %o A126119 (PARI) {a(n)= if(n<0, 0, n!* polcoeff( (1+2*x)/ (1-2*x +x*O(x^n))^(3/2), n))} /* _Michael Somos_, Apr 08 2007 */ %Y A126119 Cf. A001174, A126115. %K A126119 nonn,frac %O A126119 0,2 %A A126119 _N. J. A. Sloane_, Mar 22 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE