A260659 Denominators of a BBP-like formula for 4*Pi/sqrt(27).

2, 80, 3584, 1760, 745472, 4456448, 99614720, 265289728, 10905190400, 54492397568, 1065151889408, 1277752770560, 96619584290816, 450799767388160, 8321103999008768, 19017153114013696, 689613692941107200, 3102980143258271744, 55484347409204510720, 30822635849723674624

Offset: 0

Author

David Brink, Nov 13 2015

Keywords

• nonn
• frac

Comments

4*Pi/sqrt(27) = Sum_{n >= 0} (-1/8)^n*(2/(3*n+1)+1/(3*n+2)).

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• David H. Bailey, A Compendium of BBP-Type Formulas for Mathematical Constants.
• David Brink, Nilakantha's accelerated series for pi, Acta Arith. 171 (2015), 293-308.

Crossrefs

Cf. A073010, A260658 (numerators).

Programs

Magma

[Denominator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))): n in [0..60]]; // Vincenzo Librandi, Nov 20 2015

Mathematica

A260659[n_] := Denominator[(-1/8)^n*(2/(3*n + 1) + 1/(3*n + 2))];
Array[A260659, 25, 0] (* Paolo Xausa, Jun 19 2024 *)

PARI

a(n) = denominator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))); \\ Michel Marcus, Nov 15 2015

Formula

a(n) = denominator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))).

Extensions

More terms from Michel Marcus, Nov 15 2015