A112935 - OEIS

%I #14 Feb 17 2017 07:47:52

%S 1,3,13,79,641,6579,81677,1187039,19728193,368562723,7639512013,

%T 173893382575,4310656806977,115569893763411,3331588687405133,

%U 102751933334045375,3375782951798785921,117693183724386637635

%N Logarithmic derivative of A112934 such that a(n)=(1/2)*A112934(n+1) for n>0, where A112934 equals the INVERT transform of double factorials A001147.

%F G.f.: log(1 + x + 2*x*[Sum_{n>=1} a(n)*x^n]) = Sum_{k>=1} a(n)/n*x^n.

%F G.f.: (1 - 1/Q(0))/x where Q(k) = 1 - x*(2*k-1)/(1 - x*(2*k+4)/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Mar 19 2013

%F G.f.: 1/(x*G(0)) - 1/(2*x), where G(k)= 1 + 1/(1 - 2*x*(2*k+2)/(2*x*(2*k+2) - 1 + 2*x*(2*k+1)/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 31 2013

%e log(1+x + 2*x*[x + 3*x^2 + 13*x^3 + 79*x^4 + 641*x^5 +...])

%e = x + 3/2*x^2 + 13/3*x^3 + 79/4*x^4 + 641/5*x^5 +...

%o (PARI) {a(n)=local(F=1+x+x*O(x^n));for(i=1,n,F=1+x+2*x^2*deriv(F)/F); return(n*polcoeff(log(F),n,x))}

%Y Cf. A001147, A112934; A112936, A112937, A112938, A112939, A112940, A112941, A112942, A112943.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 09 2005