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

1,3

Comments

p^2 divides a(2p-2) for prime p>3. a(2p-2)/p^2 = A061002(n) = A001008(p-1)/p^2 for prime p>2. - Alexander Adamchuk, Jul 07 2006

Links

Robert Israel, Table of n, a(n) for n = 1..2000

N. J. A. Sloane, Transforms

Formula

G.f. for A035048(n)/A035047(n) : log(1-x)/(x^2-1). - Benoit Cloitre, Jun 15 2003

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

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

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 *)

Prog

(PARI) a(n)=numerator(polcoeff(log(1-x)/(x^2-1)+O(x^(n+1)), n))

Crossrefs

Cf. A035047, A002428, A001008, A058313, A061002.

Sequence in context: A259229 A052039 A243661 * A192857 A286671 A288434

Adjacent sequences: A035045 A035046 A035047 * A035049 A035050 A035051

Keyword

nonn,easy,frac

Author

N. J. A. Sloane.

Status

approved