A374608 a(n) is the denominator of (1134*n^3 + 2097*n^2 + 1188*n + 193)/(10368*n^4 + 20736*n^3 + 14112*n^2 + 3744*n + 320).

320, 12320, 396032, 24035, 4222400, 2360960, 18446720, 511313, 54017600, 21079520, 125864960, 5660830, 252900032, 86027840, 458015360, 18690490, 768084800, 242991008, 1213963520, 23415035, 1830488000, 553679360, 2656476032, 49394345, 3734726720, 1095728480, 5112020480

Offset: 0

Author

Paolo Xausa, Jul 13 2024

Keywords

• nonn
• frac

Comments

See Bailey and Crandall (2001), section 5 (pp. 183-185) for a derivation of this rational polynomial.

Numerators are given by A374607.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• David H. Bailey and Richard E. Crandall, On the Random Character of Fundamental Constant Expansions, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (preprint draft).

Crossrefs

Cf. A000796, A010482, A089357, A374335, A374581, A374607 (numerators).

Programs

Mathematica

A374608[n_] := Denominator[(1134*n^3 + 2097*n^2 + 1188*n + 193)/(10368*n^4 + 20736*n^3 + 14112*n^2 + 3744*n + 320)];
Array[A374608, 50, 0]

Python

from math import gcd
def A374608(n): return (q:=n*(n*(n*(324*n + 648) + 441) + 117) + 10<<5)//gcd(n*(n*(1134*n + 2097) + 1188) + 193,q) # Chai Wah Wu, Jul 14 2024

Formula

sqrt(27)*(Sum_{n >= 0} (1/64^n)*A374607(n)/a(n)) = A000796. See Bailey and Crandall (2001), p. 185.