|
| |
|
|
A072913
|
|
Numerators 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
| |
|
|
1, 31, 3661, 76111, 58067611, 68165041, 187059457981, 3355156783231, 300222042894631, 327873266234371, 5194481903600608411, 5578681466128739761, 170044702211669500782121, 180514164422163370751221
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(n) is also the numerator of binomial transform of (-1)^n/(n+1)^5
|
|
|
FORMULA
| Numerators 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))).
For n>=1, 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)=integral(x^(n-1)*(ln(1-x))^4 dx, x=0..1)
|
|
|
PROG
| (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)=numerator(1/4!*(x(n)^4+6*x(n)^2*y(n)+8*x(n)*z(n)+3*y(n)^2+6*w(n)))
|
|
|
CROSSREFS
| Cf. A027459, A027462, A072914.
Sequence in context: A106205 A174584 A183783 * A001237 A177465 A115736
Adjacent sequences: A072910 A072911 A072912 * A072914 A072915 A072916
|
|
|
KEYWORD
| easy,nonn,frac
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2002
|
|
|
EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 13 2002
|
| |
|
|
