A128560 a(n) = numerator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...,r(n)] = n^2, for every positive integer n.

1, 1, -24, 20, -112, 500, -4312, 780, -189728, 103428, -643720, 586092, -16074608, 63493300, -3882017832, 17704862500, -112528101312, 349139888500, -832452204024, 11690656900, -3884776952112, 1364209732100, -306249916391496, 279662995080500, -1531060188069792

Offset

1,3

Links

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

Formula

For n >= 4, r(n) = -16*(n-1)*(n-2)/((2n-1)*(2n-5)*r(n-1)).

Example

4^2 = 16 = 1 + 1/(1/3 +1/(-24/5 + 21/20)).
5^2 = 25 = 1 + 1/(1/3 +1/(-24/5 + 1/(20/21 -25/112))).

Maple

L2cfrac := proc(L, targ) local a, i; a := 1/(targ-op(1, L)) ; for i from 2 to nops(L) do a := 1/(a-op(i, L)) ; od: RETURN(a) ; end: A128560 := proc(nmax) local b, n, bnxt; b := [1] ; for n from 2 to nmax do bnxt := L2cfrac(b, n^2) ; b := [op(b), bnxt] ; od: [seq( numer(b[i]), i=1..nops(b))] ; end: A128560(30) ; # R. J. Mathar, Oct 09 2007

Crossrefs

Cf. A128561.

Sequence in context: A357970 A357973 A357971 * A230340 A292102 A022980

Adjacent sequences: A128557 A128558 A128559 * A128561 A128562 A128563

Keyword

sign,frac

Author

Leroy Quet, Mar 10 2007

Extensions

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

Status

approved