A124236 - OEIS

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).

%I #21 Feb 28 2024 13:21:36

%S 2,3,144,30240,4725,7983360,108972864000,8072064000,453682944000,

%T 403179783552000,1250891123328000,179527894020034560000,

%U 42009527200688087040000,9335450489041797120000

%N 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).

%H R. J. Mathar, <a href="/A124236/b124236.txt">Table of n, a(n) for n = 1..30</a>

%t 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 *)

%o (PARI) H(n)={ if(n==0, 0, sum(k=1,n,1/k)) ; }

%o A124236(n)={ denominator(sum(k=1,n,H(2*k)*(2*k)!/k!/(k+n+1)!)) ; }

%o A124236alt(n)={ denominator(sum(k=0,n-1,H(n-k)*(2*k)!/k!/(k+n+1)!)) ; } \\ _R. J. Mathar_, Oct 23 2006

%Y Cf. A124235 (numerators).

%K frac,nonn

%O 1,1

%A _Leroy Quet_, Oct 22 2006

%E Extended by _R. J. Mathar_ and _Ray Chandler_, Oct 23 2006