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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).
4
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
0,1
COMMENTS
See Bailey and Crandall (2001), section 5 (pp. 183-185) for a derivation of this rational polynomial.
Numerators are given by A374607.
LINKS
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).
FORMULA
sqrt(27)*(Sum_{n >= 0} (1/64^n)*A374607(n)/a(n)) = A000796. See Bailey and Crandall (2001), p. 185.
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]
PROG
(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
CROSSREFS
Cf. A000796, A010482, A089357, A374335, A374581, A374607 (numerators).
Sequence in context: A237326 A055863 A168636 * A264140 A045813 A121011
KEYWORD
nonn,frac
AUTHOR
Paolo Xausa, Jul 13 2024
STATUS
approved