A374580 a(n) is the numerator of (120*n^2 + 151*n + 47)/(512*n^4 + 1024*n^3 + 712*n^2 + 194*n + 15).

47, 106, 829, 316, 857, 3802, 5273, 776, 1787, 11126, 4519, 16228, 19139, 1486, 25681, 29312, 3687, 37294, 8329, 15412, 51067, 56138, 20483, 2680, 72791, 8758, 85093, 91604, 6557, 105346, 112577, 40016, 127759, 27142, 15989, 152332, 161003, 56638, 35813, 188456

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.

Denominators are given by A374581.

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, A374334, A374581 (denominators), A374607.

Programs

Mathematica

A374580[n_] := Numerator[(120*n^2 + 151*n + 47)/(512*n^4 + 1024*n^3 + 712*n^2 + 194*n + 15)];
Array[A374580, 50, 0]

Python

from math import gcd
def A374580(n): return (lambda p,q: p//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)*a(n)/A374581(n) = A000796. See Bailey and Crandall (2001), eq. 5-2, p. 184.