A262022 Denominator of partial sums of a reordered alternating harmonic series.

1, 3, 6, 30, 210, 420, 1260, 13860, 13860, 180180, 180180, 360360, 6126120, 116396280, 23279256, 23279256, 535422888, 535422888, 13385572200, 40156716600, 40156716600, 1164544781400, 36100888223400, 72201776446800, 72201776446800

Offset: 0

Author

Wolfdieter Lang, Sep 08 2015

Keywords

• nonn
• frac
• easy

Comments

See A262031 for this reordered alternating harmonic series with partial sums s(n).

Examples

			See A262031 for s(n), n=0..11, and s(10^n) for n=0..6.
		

Crossrefs

Cf. A262031, A262023.

Programs

PARI

lista(nn) = {my(s = 0); for (k=0, nn, if (k%3==2, t = -3/(2*(k+1)), if (k%3==1, t = 3/(4*k+5), t = 3/(4*k+3))); s += t; print1(denominator(s), ", "););} \\ Michel Marcus, Sep 13 2015

Formula

a(n) = denominator(s(n)) with s(n) = Sum_{k=0..n} c(k), where c(k) = 3/(4*k+3), 3/(4*k+5), -3/(2*(k+1)) if k == 0, 1, 2 (mod 3), respectively.