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).

1, 1, 17, 877, 26, 6827, 12310607, 105059, 604489, 49568347, 12933671, 143562866581, 2406858923083, 35714915113, 530084035699, 7390807289267, 1031992153425439, 225749374968517, 8052704479475951909

Offset

1,3

Links

R. J. Mathar, Table of n, a(n) for n = 1..30

Mathematica

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 *)

Prog

(PARI) H(n)={ if(n==0, 0, sum(k=1, n, 1/k)) ; }
A124235(n)={ numerator(sum(k=1, n, H(2*k)*(2*k)!/k!/(k+n+1)!)) ; }
A124235alt(n)={ numerator(sum(k=0, n-1, H(n-k)*(2*k)!/k!/(k+n+1)!)) ; } \\ R. J. Mathar, Oct 23 2006

Crossrefs

Cf. A124236 (denominators).

Sequence in context: A355468 A281428 A221324 * A218660 A086265 A156138

Adjacent sequences: A124232 A124233 A124234 * A124236 A124237 A124238

Keyword

frac,nonn

Author

Leroy Quet, Oct 22 2006

Extensions

Extended by R. J. Mathar and Ray Chandler, Oct 23 2006

Status

approved