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Search: id:A087751
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| A087751 |
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Weighted sum of the harmonic numbers. |
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+0
1
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| 0, 1, 7, 56, 538, 6124, 81048, 1226112, 20902992, 396857376, 8308373760, 190212376320, 4728556327680, 126865966625280, 3654264347274240, 112484501485977600, 3685202487258163200, 128039255560187596800
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = 2*n*a(n-1) + (n-1)!*(2^n-1); a(0)=0, a(1)=1. a(n)=n! * sum(j=1, n, binomial(n, j)*H(j)), where H(j)=sum(k=1, j, 1/k).
E.g.f.: ln((2*x-1)/(x-1))/(2*x-1). a(n) = n!*Sum_{k=1..n} (-1)^(k+1)*2^(n-k)*binomial(n, k)/k. a(n) = n!*Sum_{k=1..n} 2^(n-k)*(2^k-1)/k. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 12 2005
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PROGRAM
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(PARI) H(n)=sum(j=1, n, 1/j); a(n)=n!*sum(j=1, n, binomial(n, j)*H(j))
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CROSSREFS
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Cf. A103213, A068102.
Sequence in context: A082305 A144263 A001730 this_sequence A099345 A110830 A042187
Adjacent sequences: A087748 A087749 A087750 this_sequence A087752 A087753 A087754
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KEYWORD
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easy,nonn
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AUTHOR
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Nicholas C. Singer (nsinger2(AT)cox.net), Oct 02 2003
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