Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Jul 22 2017 08:35:47
%S 1,1,17,877,26,6827,12310607,105059,604489,49568347,12933671,
%T 143562866581,2406858923083,35714915113,530084035699,7390807289267,
%U 1031992153425439,225749374968517,8052704479475951909
%N a(n) = numerator 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="/A124235/b124235.txt">Table of n, a(n) for n = 1..30</a>
%t f[n_] := Numerator[Sum[HarmonicNumber[2k]*Factorial[2k]/(Factorial[k]*Factorial[k + n + 1]), {k, n}]];Table[f[n], {n, 21}] (* _Ray Chandler_, Oct 23 2006 *)
%o (PARI) H(n)={ if(n==0, 0, sum(k=1,n,1/k)) ; }
%o A124235(n)={ numerator(sum(k=1,n,H(2*k)*(2*k)!/k!/(k+n+1)!)) ; }
%o A124235alt(n)={ numerator(sum(k=0,n-1,H(n-k)*(2*k)!/k!/(k+n+1)!)) ; } \\ _R. J. Mathar_, Oct 23 2006
%Y Cf. A124236 (denominators).
%K frac,nonn
%O 1,3
%A _Leroy Quet_, Oct 22 2006
%E Extended by _R. J. Mathar_ and _Ray Chandler_, Oct 23 2006