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.

1, 7, 73, 1039, 18961, 423703, 11208793, 342414367, 11855713825, 458600785447, 19594307026537, 916242295851055, 46533732766792753, 2550471781317027127, 150035539128333384313, 9428390893356604340287, 630318228814408172573761

Offset: 1

Author

Paul D. Hanna, Oct 09 2005

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

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))}

Formula

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

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