A072973 Denominator of b(n) = (50*n-6)/(binomial(3n,n)*2^n).

1, 3, 30, 14, 3960, 24024, 28288, 1860480, 94140288, 199971200, 1183311360, 12386350080, 284826214400, 2376389615616, 433030996623360, 15188999733248, 73886889202384896, 484018391833804800, 4234776786964971520, 20872690706733465600, 313961967465678766080, 55480990606260961280

Offset

0,2

Comments

A powerful series to compute Pi via the Beta method. Proved first by Almkvist, Krattenthaler, and Petersson (2003).

Links

Table of n, a(n) for n=0..21.

Gert Almkvist, Christian Krattenthaler, and Joakim Petersson, Some new formulas for Pi, Experimental Mathematics, Vol. 12, No. 4 (2003), pp. 441-456; alternative link.

Formula

Sum_{k>=0} b(k) = Pi.

Mathematica

a[n_] := Denominator[(50*n-6)/(2^n * Binomial[3*n, n])]; Array[a, 20, 0] (* Amiram Eldar, Apr 28 2025 *)

Prog

(PARI) a(n)=denominator((50*n-6)/binomial(3*n, n)/2^n)

Crossrefs

Cf. A072972 (numerators).

Sequence in context: A082792 A078242 A108739 * A154054 A118219 A186681

Adjacent sequences: A072970 A072971 A072972 * A072974 A072975 A072976

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Aug 13 2002

Status

approved