A329304 - OEIS

%I #12 Dec 05 2019 04:20:27

%S 0,1,8,217,13896,1737217,375252768,128713436641,65901654812960,

%T 48042435072084481,48042500973739293960,63944616838482072345241,

%U 110496345939397994751870408,242760535973474232951931631617,666135021207559234618095149027456

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>

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

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

%o (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

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

%K nonn,frac

%O 0,3

%A _Jianing Song_, Nov 30 2019