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A078736 Numerators of convergents to sqrt(e). 1
1, 2, 3, 5, 28, 33, 61, 582, 643, 1225, 16568, 17793, 34361, 601930, 636291, 1238221, 26638932, 27877153, 54516085, 1390779278, 1445295363, 2836074641, 83691459952, 86527534593, 170218994545, 5703754354578, 5873973349123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..27.

FORMULA

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

MATHEMATICA

Numerator[Convergents[Sqrt[E], 30]] (* Harvey P. Dale, Sep 23 2011 *)

PROG

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

CROSSREFS

Cf. A058281, A078737, A065919.

Sequence in context: A121264 A141566 A247094 * A042669 A178376 A041585

Adjacent sequences:  A078733 A078734 A078735 * A078737 A078738 A078739

KEYWORD

frac,nonn

AUTHOR

Benoit Cloitre, Dec 20 2002

STATUS

approved

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Last modified December 7 20:33 EST 2019. Contains 329849 sequences. (Running on oeis4.)