A242376 Numerators of b(n) = b(n-1)/2 + 1/(2*n), b(0)=0.

0, 1, 1, 5, 1, 4, 13, 151, 16, 83, 73, 1433, 647, 15341, 28211, 10447, 608, 19345, 18181, 651745, 771079, 731957, 2786599, 122289917, 14614772, 140001721, 134354573, 774885169, 745984697, 41711914513, 80530073893, 4825521853483

Offset

0,4

Comments

See the denominators in A241519.

b(n) = 0, 1/2, 1/2, 5/12, 1/3, 4/15, 13/60, 151/840, 16/105, 83/630, 73/630, ... (Ta0(n) in A241269) is an autosequence of the first kind.

Links

Ralf Stephan, Table of n, a(n) for n = 0..999

Formula

0 = b(n)*(+b(n+1) - 4*b(n+2) + 4*b(n+3)) + b(n+1)*(-2*b(n+1) + 9*b(n+2) - 10*b(n+3)) + b(n+2)*(-2*b(n+2) + 4*b(n+3)) if n>=0. - Michael Somos, May 26 2014

b(n) = -Re(Phi(2, 1, n + 1)). - Eric W. Weisstein, Dec 11 2017

G.f. for b(n): -log(1-x)/(2*(1-x/2)). - Vladimir Kruchinin, Nov 14 2022

Example

0, 1/2, 1/2, 5/12, 1/3, 4/15, 13/60, 151/840, 16/105, 83/630, 73/630, ...

Mathematica

Table[-Re[LerchPhi[2, 1, n + 1]], {n, 0, 20}] // Numerator (* Eric W. Weisstein, Dec 11 2017 *)
-Re[LerchPhi[2, 1, Range[20]]] // Numerator (* Eric W. Weisstein, Dec 11 2017 *)
RecurrenceTable[{b[n] == b[n - 1]/2 + 1/(2 n), b[0] == 0}, b[n], {n, 20}] // Numerator (* Eric W. Weisstein, Dec 11 2017 *)

Prog

(Sage)
def a():
    b = n = 0
    while True:
        yield numerator(b)
        n = n + 1
        b = (b/2 + 1/(2*n)) # Ralf Stephan, May 18 2014

Crossrefs

Cf. A241519 (denominators).

Sequence in context: A316248 A180132 A286593 * A307393 A231923 A105664

Adjacent sequences: A242373 A242374 A242375 * A242377 A242378 A242379

Keyword

nonn,frac

Author

Paul Curtz, May 12 2014

Extensions

a(14)-a(25) from Jean-François Alcover, May 12 2014

Corrected a(22) and a(24), more terms from Ralf Stephan, May 18 2014

Status

approved