A035048 Numerators of alternating sum transform (PSumSIGN) of Harmonic numbers H(n) = A001008/A002805.
1, 1, 4, 3, 23, 11, 176, 25, 563, 137, 6508, 49, 88069, 363, 91072, 761, 1593269, 7129, 31037876, 7381, 31730711, 83711, 744355888, 86021, 3788707301, 1145993, 11552032628, 1171733, 340028535787, 1195757
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..2000
- N. J. A. Sloane, Transforms
Programs
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Maple
S:= series(log(1-x)/(x^2-1), x, 101): seq(numer(coeff(S,x,j)), j=1..100); # Robert Israel, Jun 02 2015
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Mathematica
Numerator[Table[Sum[(-1)^(k+1)*Sum[(-1)^(i+1)*1/i,{i,1,k}],{k,1,n}],{n,1,50}]] (* Alexander Adamchuk, Jul 07 2006 *) -
PARI
a(n)=numerator(polcoeff(log(1-x)/(x^2-1)+O(x^(n+1)),n))
Formula
a(n) = Numerator[Sum[(-1)^(k+1)*Sum[(-1)^(i+1)*1/i,{i,1,k}],{k,1,n}]]. - Alexander Adamchuk, Jul 07 2006
a(n) = numerator((-1)^(n+1)*1/2*(log(2)+(-1)^(n+1)*(gamma+1/2*(psi(1+n/2)-psi(3/2+n/2))+psi(2+n)))), with gamma the Euler-Mascheroni constant. - - Gerry Martens, Apr 28 2011
Comments