A112941 Logarithmic derivative of A112940 such that a(n)=(1/5)*A112940(n+1) for n>0, where A112940 equals the INVERT transform (with offset) of quintuple factorials A008546.

1, 9, 121, 2209, 51401, 1457649, 48774041, 1880312129, 82028211241, 3993290362449, 214543742998201, 12606663551853409, 804145149477634121, 55332318403485181809, 4084986234723143402201, 322064057582671115832449

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Formula

G.f.: log(1+x + 5*x*[Sum_{n>=1} a(n)]) = Sum_{n>=1} a(n)/n*x^n.

Example

log(1+x + 5*x*[x + 9*x^2 + 121*x^3 + 2209*x^4 + 51401*x^5 +...])
= x + 9/2*x^2 + 121/3*x^3 + 2209/4*x^4 + 51401/5*x^5 + ...

Prog

(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+5*x^2*deriv(F)/F); return(n*polcoeff(log(F), n, x))}

Crossrefs

Cf. A008546, A112940; A112934, A112935, A112936, A112937, A112938, A112939, A112942, A112943.

Sequence in context: A202835 A321847 A050353 * A352119 A258380 A360547

Adjacent sequences: A112938 A112939 A112940 * A112942 A112943 A112944

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2005

Status

approved