|
|
A124236
|
|
a(n) = denominator of (Sum_{k=1..n} H(2k)(2k)!/(k!(k+n+1)!) = Sum_{k=0..n-1} H(n-k)(2k)!/ (k!(k+n+1)!)), where H(k) = Sum_{j=1..k} 1/j (i.e., the k-th harmonic number).
|
|
2
|
|
|
2, 3, 144, 30240, 4725, 7983360, 108972864000, 8072064000, 453682944000, 403179783552000, 1250891123328000, 179527894020034560000, 42009527200688087040000, 9335450489041797120000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
MATHEMATICA
|
f[n_] := Denominator[Sum[HarmonicNumber[2k]*Factorial[2k]/(Factorial[k]*Factorial[k + n + 1]), {k, n}]]; Table[f[n], {n, 16}] (* Ray Chandler, Oct 23 2006 *)
|
|
PROG
|
(PARI) H(n)={ if(n==0, 0, sum(k=1, n, 1/k)) ; }
A124236(n)={ denominator(sum(k=1, n, H(2*k)*(2*k)!/k!/(k+n+1)!)) ; }
A124236alt(n)={ denominator(sum(k=0, n-1, H(n-k)*(2*k)!/k!/(k+n+1)!)) ; } \\ R. J. Mathar, Oct 23 2006
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|