A121005 Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/125.

1, 125, 15625, 390625, 244140625, 30517578125, 3814697265625, 476837158203125, 11920928955078125, 7450580596923828125, 931322574615478515625, 116415321826934814453125, 14551915228366851806640625, 72759576141834259033203125, 45474735088646411895751953125, 5684341886080801486968994140625

Offset

0,2

Comments

See A121004.

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = denominator(r(n)) with r(n) = rII(p=2,n) = Sum_{k=0..n} C(k)/5^(3*k) and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.

Example

Rationals r(n): [1, 126/125, 15752/15625, 393801/390625, 246125639/244140625, 30765704917/30517578125, ...].

Prog

(PARI) a(n) = denominator(sum(k=0, n, binomial(2*k, k)/(k+1) / 5^(3*k))); \\ Michel Marcus, Feb 28 2026

Crossrefs

Cf. A121004 (numerators).

Sequence in context: A347510 A275296 A259925 * A264062 A067972 A094197

Adjacent sequences: A121002 A121003 A121004 * A121006 A121007 A121008

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Aug 16 2006

Extensions

More terms from Michel Marcus, Feb 28 2026

Status

approved