A076174 Numerator of Sum_{i+j+k=n, i,j,k>=1} (i*j)/k.

0, 0, 1, 9, 37, 319, 743, 2509, 2761, 32891, 35201, 485333, 511073, 535097, 1115239, 19679783, 6786821, 133033679, 136913555, 140608675, 144135835, 678544345, 693417203, 17692378667, 18035598467, 165294957803, 168163294703

Offset: 1

Author

Benoit Cloitre, Nov 01 2002

Keywords

• frac
• nonn

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

Crossrefs

Cf. A076175.

Cf. A124837 = Numerators of third-order harmonic numbers (defined by Conway and Guy, 1996).

Programs

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 *)

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))))

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