A374607 a(n) is the numerator of (1134*n^3 + 2097*n^2 + 1188*n + 193)/(10368*n^4 + 20736*n^3 + 14112*n^2 + 3744*n + 320).

193, 1153, 20029, 832, 111073, 50077, 327757, 7816, 724513, 251857, 1355773, 55511, 2275969, 715357, 3539533, 134909, 5200897, 1549441, 7314493, 133717, 9934753, 2862973, 13116109, 233347, 16912993, 4764817, 21379837, 746297, 26571073, 7363837, 32541133, 1119851

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.

Denominators are given by A374608.

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, A374334, A374580, A374608 (denominators).

Programs

Mathematica

A374607[n_] := Numerator[(1134*n^3 + 2097*n^2 + 1188*n + 193)/(10368*n^4 + 20736*n^3 + 14112*n^2 + 3744*n + 320)];
Array[A374607, 50, 0]

Python

from math import gcd
def A374607(n): return (p:=n*(n*(1134*n + 2097) + 1188) + 193)//gcd(p,n*(n*(n*(324*n + 648) + 441) + 117) + 10<<5) # Chai Wah Wu, Jul 14 2024

Formula

sqrt(27)*(Sum_{n >= 0} (1/64^n)*a(n)/A374608(n)) = A000796. See Bailey and Crandall (2001), p. 185.