A329305 Denominators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, ...].

1, 1, 9, 244, 15625, 1953369, 421943329, 144728515216, 74101421733921, 54020081172543625, 54020155273965358921, 71900880689729065267476, 124244775852007098747557449, 272965844447740285677448982929, 749018401409375195906018756714625

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Eric Weisstein's World of Mathematics, Continued Fraction

Formula

a(0) = 1, a(1) = 1, a(n) = n^3*a(n-1) + a(n-2) for n >= 2.

Example

Convergents to [0; 1, 8, 27, 64, ...]: 0, 1, 8/9, 217/244, 13896/15625, 1737217/1953369, 375252768/421943329, ...

Prog

(PARI) A329305_up_to_n(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=1, if(i==2, v[i]=1, v[i]=(i-1)^3*v[i-1]+v[i-2]))); v

Crossrefs

Cf. A309930, A329304 (numerators), A001040, A036246.

Sequence in context: A167005 A112028 A368769 * A183235 A359732 A259673

Adjacent sequences: A329302 A329303 A329304 * A329306 A329307 A329308

Keyword

nonn,frac

Author

Jianing Song, Nov 30 2019

Status

approved