A078977 Denominator of n-th convergent to e^(2/3).

1, 1, 19, 134, 153, 287, 3023, 163529, 2619487, 2783016, 5402503, 105430573, 9494154073, 237459282398, 246953436471, 484412718869, 13810509564803, 1740608617884047, 59194503517622401, 60935112135506448

Offset: 1

Author

Benoit Cloitre, Dec 19 2002

Keywords

• frac
• nonn

Crossrefs

Cf. A069951, A065923, A001518, A007677, A078976.

Programs

Mathematica

Denominator[Convergents[E^(2/3),20]] (* Harvey P. Dale, Dec 01 2013 *)

PARI

a(n)=component(component(contfracpnqn(contfrac(exp(2/3),n)),1),2) \\ (Warning: this will give only a limited number of correct terms, depending on the precision used. - The Editors, Oct 13 2009. See A078976 for better code.)

Formula

Special cases : a(5k+1)=abs(A065923(3k)); a(5k+3)=abs(A065923(3k+2)) where A065923(n)=y(n, -3) where y(n, x)=sum (k=0, n, (n+k)!*(x/2)^k/((n-k)!*k!))