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A124235 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). 2

%I

%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

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Last modified June 15 09:57 EDT 2021. Contains 345048 sequences. (Running on oeis4.)