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%I #17 Mar 14 2015 01:59:37
%S 0,0,1,9,37,319,743,2509,2761,32891,35201,485333,511073,535097,
%T 1115239,19679783,6786821,133033679,136913555,140608675,144135835,
%U 678544345,693417203,17692378667,18035598467,165294957803,168163294703
%N Numerator of sum( i+j+k = n, (i*j)/k) i,j,k >=1.
%C a(n) is odd.
%C a(n+2) = Numerators of 4th-order harmonic numbers (defined by Conway and Guy, 1996). - _Alexander Adamchuk_, Jun 14 2008
%D J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, pp. 143 and 258-259, 1996.
%H Alexander Adamchuk, Jun 14 2008, <a href="/A076174/b076174.txt">Table of n, a(n) for n = 1..52</a>
%F 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
%F a(n) = Numerator(sum(1/(k+3), k=1..n-2)), n>1. - _Gary Detlefs_, Sep 14 2011
%t 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 *)
%o (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))))
%Y Cf. A076175.
%Y Cf. A124837 = Numerators of third-order harmonic numbers (defined by Conway and Guy, 1996).
%K frac,nonn
%O 1,4
%A _Benoit Cloitre_, Nov 01 2002
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