A078737 Denominators of convergents to sqrt(e).

1, 1, 2, 3, 17, 20, 37, 353, 390, 743, 10049, 10792, 20841, 365089, 385930, 751019, 16157329, 16908348, 33065677, 843550273, 876615950, 1720166223, 50761436417, 52481602640, 103243039057, 3459501891521, 3562744930578, 7022246822099

Offset

1,3

Links

Table of n, a(n) for n=1..28.

Formula

Let y(n, x)=sum(k=0, n, (n+k)!*(x/2)^k/((n-k)!*k!)) then : a(3*n-1)=(1/2)*(|y(n, -4)|- |y(n-1, -4)|); a(3*n)=(1/2)*(|y(n, -4)|+ |y(n-1, -4)|); a(3*n+1)=|y(n, -4)|

Prog

(PARI) a(n)=component(component(contfracpnqn(contfrac(exp(1/2), n)), 1), 2)

Crossrefs

Cf. A058281, A078736, A065919.

Sequence in context: A041295 A128845 A128851 * A041981 A197223 A045342

Adjacent sequences: A078734 A078735 A078736 * A078738 A078739 A078740

Keyword

frac,nonn

Author

Benoit Cloitre, Dec 20 2002

Status

approved