A374581 a(n) is the denominator of (120*n^2 + 151*n + 47)/(512*n^4 + 1024*n^3 + 712*n^2 + 194*n + 15).

15, 819, 19635, 15225, 69597, 466785, 911547, 179645, 533715, 4165161, 2072385, 8947437, 12491175, 1133055, 22621131, 29539125, 4214903, 48002745, 11990775, 24669567, 90400695, 109375617, 43730505, 6244749, 184439871, 24049985, 252455907, 292777485, 22516425, 387706641

Offset: 0

Author

Paolo Xausa, Jul 12 2024

Keywords

• nonn
• frac

Comments

See Bailey and Crandall (2001), section 5 (pp. 183-184) for a derivation of this rational polynomial.

Numerators are given by A374580.

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, A001025, A374335, A374580 (numerators), A374608.

Programs

Mathematica

A374581[n_] := Denominator[(120*n^2 + 151*n + 47)/(512*n^4 + 1024*n^3 + 712*n^2 + 194*n + 15)];
Array[A374581, 30, 0]

Python

from math import gcd
def A374581(n): return (lambda p,q: q//gcd(p,q))(n*(120*n + 151) + 47,n*(n*(n*(512*n + 1024) + 712) + 194) + 15) # Chai Wah Wu, Jul 14 2024

Formula

Sum_{n >= 0} (1/16^n)*A374580(n)/a(n) = A000796. See Bailey and Crandall (2001), eq. 5-2, p. 184.