A128536 a(n) = numerator 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, 1, -10, 21, -16, 165, -1664, 2625, -34816, 41895, -32768, 334719, -6553600, 2675673, -60817408, 85579065, -67108864, 2737609875, -79456894976, 21895664505, -704374636544, 175134692733, -687194767360, 2801784820107, -2199023255552, 44823971549175

Offset

1,3

Links

Table of n, a(n) for n=1..26.

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: A128536 := 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( numer(b[i]), i=1..nops(b))] ; end: A128536(26) ; # R. J. Mathar, Oct 09 2007

Crossrefs

Cf. A128537.

Sequence in context: A085222 A085221 A341111 * A202318 A251128 A244539

Adjacent sequences: A128533 A128534 A128535 * A128537 A128538 A128539

Keyword

frac,sign

Author

Leroy Quet, Mar 09 2007

Extensions

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

Status

approved