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

1,2

Links

Table of n, a(n) for n=1..17.

Formula

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

Example

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 + ...

Prog

(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))}

Crossrefs

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

Sequence in context: A055869 A208231 A352117 * A258378 A368322 A273954

Adjacent sequences: A112934 A112935 A112936 * A112938 A112939 A112940

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2005

Status

approved