

A128537


a(n) = denominator of r(n): r(n) is such that, for every positive integer n, the continued fraction (of rational terms) [r(1);r(2),...,r(n)] equals n(n+1)/2, the nth triangular number.


2



1, 2, 3, 16, 5, 128, 525, 2048, 11025, 32768, 10395, 262144, 2081079, 2097152, 19324305, 67108864, 21332025, 2147483648, 25264228275, 17179869184, 224009490705, 137438953472, 218578957597, 2199023255552, 699533769675
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..25.


FORMULA

For n >=4, r(n) = (2n1)*(2n3)/(n(n2) r(n1)).


EXAMPLE

The 4th triangular number, 10, equals 1 +(1/2 +1/(10/3 +16/21)).
The 5th triangular number, 15, equals 1 +(1/2 +1/(10/3 +1/(21/16 5/16))).


MAPLE

L2cfrac := proc(L, targ) local a, i; a := targ ; for i from 1 to nops(L) do a := 1/(aop(i, L)) ; od: end: A128537 := proc(nmax) local b, n, bnxt; b := [1] ; for n from nops(b)+1 to nmax do bnxt := L2cfrac(b, n*(n+1)/2) ; b := [op(b), bnxt] ; od: [seq( denom(b[i]), i=1..nops(b))] ; end: A128537(26) ;  R. J. Mathar, Oct 09 2007


CROSSREFS

Cf. A128536.
Sequence in context: A167761 A176029 A218323 * A220849 A066841 A074270
Adjacent sequences: A128534 A128535 A128536 * A128538 A128539 A128540


KEYWORD

frac,nonn


AUTHOR

Leroy Quet, Mar 09 2007


EXTENSIONS

More terms from R. J. Mathar, Oct 09 2007


STATUS

approved



