A112937 Logarithmic derivative of A112936 such that a(n)=(1/3)*A112936(n+1) for n>0, where A112936 equals the INVERT transform (with offset) of triple factorials A008544.

1, 5, 37, 377, 4981, 81305, 1580797, 35637377, 913115701, 26189790425, 830916198157, 28883617580177, 1091455878504421, 44541746007215945, 1952125704702209917, 91440056107001450177, 4558596081095404198741

Offset: 1

Author

Paul D. Hanna, Oct 09 2005

Keywords

• nonn

Examples

			log(1+x + 3*x*[x + 5*x^2 + 37*x^3 + 377*x^4 + 4981*x^5 +...])
= x + 5/2*x^2 + 37/3*x^3 + 377/4*x^4 + 4981/5*x^5 + ...
		

Crossrefs

Cf. A008544, A112936; A112934, A112935, A112938, A112939, A112940, A112941, A112942, A112943.

Programs

PARI

{a(n)=local(F=1+x+x*O(x^n));for(i=1,n,F=1+x+3*x^2*deriv(F)/F); return(n*polcoeff(log(F),n,x))}

Formula

G.f.: log(1+x + 3*x*[Sum_{k>=1} a(n)]) = Sum_{k>=1} a(n)/n*x^n.