A124235 - OEIS

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

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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