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A128295
a(n) = numerator of b(n): b(1)=1; b(n+1) = b(n) * [b(1);b(2),...,b(n)], where [...] is a continued fraction of rational terms.
2
1, 1, 2, 10, 560, 18393200, 11307340057302083200, 79095479027242971758816977525848827652668769392000
OFFSET
1,3
COMMENTS
a(9) and a(10) have 131 and 343 digits, respectively and are too large to include here. - R. J. Mathar, Oct 08 2007
EXAMPLE
a(5) = the numerator of b(5). b(5) = (10/3) * (1 +1/(1 +1/(2 +3/10))) = 560/99.
MAPLE
L2cfrac := proc(L) local a, i; a := op(-1, L) ; for i from 2 to nops(L) do a := op(-i, L)+1/a ; od: RETURN(a) ; end: A128295 := proc() local b, n, bnxt; b := [1] ; for n from 2 to 10 do bnxt := op(-1, b)*L2cfrac(b) ; b := [op(b), bnxt] ; od: [seq( numer(b[i]), i=1..nops(b))] ; end: A128295() ; # R. J. Mathar, Oct 08 2007
CROSSREFS
Cf. A128296.
Sequence in context: A064300 A290060 A087754 * A375532 A089500 A246628
KEYWORD
frac,nonn
AUTHOR
Leroy Quet, Feb 25 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 08 2007
STATUS
approved