OFFSET
1,4
COMMENTS
a(n) is odd.
a(n+2) = Numerators of 4th-order harmonic numbers (defined by Conway and Guy, 1996). - Alexander Adamchuk, Jun 14 2008
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, pp. 143 and 258-259, 1996.
LINKS
Alexander Adamchuk, Jun 14 2008, Table of n, a(n) for n = 1..52
FORMULA
a(n) = Numerator[Sum[ Sum[ Sum[ Sum[ 1/k, {k,1,l} ], {l,1,m} ], {m,1,n} ], {n,1,s-2} ] ]. a(n) = Numerator[ (n-1)n(n+1)/6 * Sum[ 1/k, {k,4,n+1} ] ]. - Alexander Adamchuk, Jun 14 2008
a(n) = Numerator(sum(1/(k+3), k=1..n-2)), n>1. - Gary Detlefs, Sep 14 2011
MATHEMATICA
Table[ Numerator[Sum[ Sum[ Sum[ Sum[ 1/k, {k, 1, l} ], {l, 1, m} ], {m, 1, n} ], {n, 1, s-2} ] ], {s, 1, 52} ] Table[ Numerator[ (n-1)n(n+1)/6 * Sum[ 1/k, {k, 4, n+1} ] ], {n, 1, 50}] (* Alexander Adamchuk, Jun 14 2008 *)
PROG
(PARI) a(n)=numerator(sum(i=1, n, sum(j=1, n, sum(k=1, n, if(n-i-j-k, 0, 1)*i*j/k))))
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Benoit Cloitre, Nov 01 2002
STATUS
approved