A329304 Numerators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, ...].

0, 1, 8, 217, 13896, 1737217, 375252768, 128713436641, 65901654812960, 48042435072084481, 48042500973739293960, 63944616838482072345241, 110496345939397994751870408, 242760535973474232951931631617, 666135021207559234618095149027456

Offset

0,3

Links

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

Eric Weisstein's World of Mathematics, Continued Fraction

Formula

a(0) = 0, 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) A329304_up_to_n(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=0, if(i==2, v[i]=1, v[i]=(i-1)^3*v[i-1]+v[i-2]))); v

Crossrefs

Cf. A309930, A329305 (denominators), A001053, A036245.

Sequence in context: A245591 A247539 A188680 * A352471 A232157 A305517

Adjacent sequences: A329301 A329302 A329303 * A329305 A329306 A329307

Keyword

nonn,frac

Author

Jianing Song, Nov 30 2019

Status

approved