A072972 Numerator of b(n) = (50*n-6)/(binomial(3n,n)*2^n).

-6, 22, 47, 3, 97, 61, 7, 43, 197, 37, 19, 17, 33, 23, 347, 1, 397, 211, 149, 59, 71, 1, 547, 11, 199, 311, 647, 1, 17, 361, 1, 193, 797, 137, 121, 109, 23, 461, 947, 9, 997, 73, 349, 67, 1097, 17, 37, 293, 19, 47, 43, 1, 1297, 661, 449, 49, 1, 1, 1447, 23, 499, 761, 17, 1, 1597, 811, 61, 209, 1697, 1, 1747, 443, 599

Offset

0,1

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..72.

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_] := Numerator[(50*n-6)/(2^n * Binomial[3*n, n])]; Array[a, 100, 0] (* Amiram Eldar, Apr 28 2025 *)

Prog

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

Crossrefs

Cf. A072973 (denominators).

Sequence in context: A015721 A182200 A370352 * A216050 A202803 A366917

Adjacent sequences: A072969 A072970 A072971 * A072973 A072974 A072975

Keyword

easy,frac,sign

Author

Benoit Cloitre, Aug 13 2002

Status

approved