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 n-th triangular number.

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

Offset

1,2

Links

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

Formula

For n >=4, r(n) = -(2n-1)*(2n-3)/(n(n-2) r(n-1)).

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/(a-op(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: A218323 A369893 A345136 * A266265 A259209 A220849

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