A072914 Denominators of 1/4!*(H(n,1)^4+6*H(n,1)^2*H(n,2)+8*H(n,1)*H(n,3)+3*H(n,2)^2+6*H(n,4)), where H(n,m) = Sum_{i=1..n} 1/i^m are generalized harmonic numbers.

1, 16, 1296, 20736, 12960000, 12960000, 31116960000, 497871360000, 40327580160000, 40327580160000, 590436101122560000, 590436101122560000, 16863445484161436160000, 16863445484161436160000

Offset: 1

Author

Vladeta Jovovic, Aug 10 2002

Keywords

• easy
• nonn
• frac

Comments

a(n) = A007480 (n) for n=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 51, 52, 53, 54, 110, 111, 112, 113, 114, 115, 116...... - Benoit Cloitre, Aug 13 2002

Crossrefs

Cf. A072913.

Programs

PARI

x(n)=sum(k=1,n,1/k); y(n)=sum(k=1,n,1/k^2); z(n)=sum(k=1,n,1/k^3); w(n)=sum(k=1,n,1/k^4); a(n)=denominator(1/4!*(x(n)^4+6*x(n)^2*y(n)+8*x(n)*z(n)+3*y(n)^2+6*w(n)))

Formula

Denominators of 1/4!*((gamma+Psi(n+1))^4+6*(gamma+Psi(n+1))^2*(1/6*Pi^2-Psi(1, n+1))+8*(gamma+Psi(n+1))*(Zeta(3)+1/2*Psi(2, n+1))+3*(1/6*Pi^2-Psi(1, n+1))^2+6*(1/90*Pi^4-1/6*Psi(3, n+1))).

Extensions

More terms from Benoit Cloitre, Aug 13 2002