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A112939 Logarithmic derivative of A112938 such that a(n)=(1/4)*A112938(n+1) for n>0, where A112938 equals the INVERT transform (with offset) of quadruple factorials A008545. 9

%I #6 Jun 04 2013 12:12:04

%S 1,7,73,1039,18961,423703,11208793,342414367,11855713825,458600785447,

%T 19594307026537,916242295851055,46533732766792753,2550471781317027127,

%U 150035539128333384313,9428390893356604340287,630318228814408172573761

%N Logarithmic derivative of A112938 such that a(n)=(1/4)*A112938(n+1) for n>0, where A112938 equals the INVERT transform (with offset) of quadruple factorials A008545.

%F G.f.: log(1+x + 4*x*[Sum_{k>=1} a(n)]) = Sum_{k>=1} a(n)/n*x^n.

%F G.f.: 1/x - G(0)/(2*x), where G(k)= 1 + 1/(1 - x*(4*k-1)/(x*(4*k-3) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 04 2013

%e log(1+x + 4*x*[x + 7*x^2 + 73*x^3 + 1039*x^4 + 18961*x^5 +...])

%e = x + 7/2*x^2 + 73/3*x^3 + 1039/4*x^4 + 18961/5*x^5 + ...

%o (PARI) {a(n)=local(F=1+x+x*O(x^n));for(i=1,n,F=1+x+4*x^2*deriv(F)/F); return(n*polcoeff(log(F),n,x))}

%Y Cf. A008545, A112938; A112934, A112935, A112936, A112937, A112940, A112941, A112942, A112943.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 09 2005

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)