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Search: id:A072913
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| A072913 |
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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. |
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| 1, 31, 3661, 76111, 58067611, 68165041, 187059457981, 3355156783231, 300222042894631, 327873266234371, 5194481903600608411, 5578681466128739761, 170044702211669500782121, 180514164422163370751221
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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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))).
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PROGRAM
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(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)))
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CROSSREFS
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Cf. A027459, A027462, A072914.
Adjacent sequences: A072910 A072911 A072912 this_sequence A072914 A072915 A072916
Sequence in context: A062987 A136245 A106205 this_sequence A001237 A115736 A110848
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KEYWORD
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easy,nonn,frac
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 10 2002
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 13 2002
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