

A078737


Denominators of convergents to sqrt(e).


1



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
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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/((nk)!*k!)) then : a(3*n1)=(1/2)*(y(n, 4) y(n1, 4)); a(3*n)=(1/2)*(y(n, 4)+ y(n1, 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



