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Search: id:A124235
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| A124235 |
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a(n) = numerator of (sum{k=1 to n} H(2k)(2k)!/(k!(k+n+1)!) = sum{k=0 to n-1} H(n-k)(2k)!/ (k!(k+n+1)!)), where H(k) = sum{j=1 to k} 1/j (i.e. the k-th harmonic number). |
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+0
2
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| 1, 1, 17, 877, 26, 6827, 12310607, 105059, 604489, 49568347, 12933671, 143562866581, 2406858923083, 35714915113, 530084035699, 7390807289267, 1031992153425439, 225749374968517, 8052704479475951909
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..30
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MATHEMATICA
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f[n_] := Numerator[Sum[HarmonicNumber[2k]*Factorial[2k]/(Factorial[k]*Factorial[k + n + 1]), {k, n}]]; Table[f[n], {n, 21}] (*Chandler*)
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PROGRAM
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(PARI) H(n)={ if(n==0, 0, sum(k=1, n, 1/k)) ; }
(PARI) A124235(n)={ numerator(sum(k=1, n, H(2*k)*(2*k)!/k!/(k+n+1)!)) ; }
(PARI) A124235alt(n)={ numerator(sum(k=0, n-1, H(n-k)*(2*k)!/k!/(k+n+1)!)) ; } (Mathar)
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CROSSREFS
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Cf. A124236.
Adjacent sequences: A124232 A124233 A124234 this_sequence A124236 A124237 A124238
Sequence in context: A012221 A012144 A139091 this_sequence A086265 A077645 A046731
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Oct 22 2006
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EXTENSIONS
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Extended by R. J. Mathar and Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 23 2006
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