A124384 - OEIS

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A124384

O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + 2^k*x).

1, 2, 4, 10, 30, 110, 494, 2734, 18734, 159278, 1685550, 22268974, 367653934, 7597868078, 196929315886, 6402998805550, 261393582040110, 13416320169124910, 865576139256079406, 70227589169019724846 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	LINKS	`Table of n, a(n) for n=0..19.`
	FORMULA	`G.f.: (G(0) - 1)/(x-1) where G(k) = 1 - (1+x*2^k)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 16 2013`
	EXAMPLE	`A(x) = (1+x) + x(1+x)(1+2x) + x^2(1+x)(1+2x)(1+4x) + x^3(1+x)(1+2x)(1+4x)*(1+8x) +...`
	PROG	`(PARI) a(n)=polcoeff(sum(k=0, n, x^kprod(j=0, k, 1+2^jx+x*O(x^n))), n)`
	CROSSREFS	`Sequence in context: A005193 A173940 A101901 * A001647 A007177 A138415` `Adjacent sequences: A124381 A124382 A124383 * A124385 A124386 A124387`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna, Oct 28 2006`
	STATUS	`approved`

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Last modified May 23 04:04 EDT 2013. Contains 225585 sequences.