A046126 - OEIS

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A046126

Denominators q[ n ] of convergents to Stern's non-simple continued fraction for Pi/2.

1, 3, -3, -15, 45, 315, -1575, -14175, 99225, 1091475, -9823275, -127702575, 1404728325, 21070924875, -273922023375, -4656674397375, 69850115960625, 1327152203251875, -22561587455281875, -473793336560919375 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	LINKS	`Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `Index entries for sequences related to Stern's sequences`
	FORMULA	`E.g.f.: exp(asinh(x))((1+x)/(1+x^2)+(2-x+x^2)/(1+x^2)^(3/2))-2. - Michael Somos Mar 11 2004`
	MATHEMATICA	`b[ n_ ] := 2-(-1)^n; a[ 1 ] := -1; a[ n_Integer?EvenQ ] := -n(n+1); a[ n_Integer?OddQ ] := -(n-2)(n-1); then use the standard algorithm to get p[ n ]/q[ n ].`
	PROG	`(PARI) a(n)=if(n<0, 0, prod(k=1, n, if(k%2, k+2, 1-k)))` `(PARI) {a(n)=local(A); if(n<0, 0, A=matrix(2, n+1); for(k=0, n, A[2, k+1]=if(k%2, 3, 1); A[1, k+1]=if(k<2, (-1)^k, if(k%2, -(k-2)(k-1), -k(k+1)))); contfracpnqn(A)[2, 1])} /* Michael Somos Jul 15 2003 */`
	CROSSREFS	`Numerators p[ n ] are (-1)^[n/2]A001900(n). See also A013069.` `Cf. A079484.` `Sequence in context: A067655 A160624 A049606 A143257 A089403 A111674` `Adjacent sequences: A046123 A046124 A046125 * A046127 A046128 A046129`
	KEYWORD	`sign,frac`
	AUTHOR	`Eric Weisstein (eric(AT)weisstein.com)`

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Last modified February 17 11:46 EST 2012. Contains 206011 sequences.