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Decimal expansion of the constant x that satisfies: F(x) - x*F'(x) = 0, where F(x) = Sum_{n>=0} x^(n*(n+1)/2).

+0
5

6, 4, 1, 1, 8, 0, 3, 8, 8, 4, 2, 9, 9, 5, 4, 5, 7, 9, 6, 4, 5, 6, 4, 4, 8, 8, 8, 6, 2, 8, 3, 0, 1, 1, 0, 6, 5, 5, 3, 4, 1, 9, 6, 1, 8, 9, 1, 0, 0, 7, 1, 1, 9, 0, 8, 7, 7, 5, 6, 0, 3, 0, 5, 0, 5, 1, 3, 1, 7, 2, 7, 8, 4, 5, 7, 5, 9, 2, 4, 7, 3, 3, 2, 3, 7, 8, 4, 6, 3, 5, 1, 2, 0, 8, 8, 3, 7, 9, 3, 2, 2, 4, 8, 9, 6 (list; cons; graph; listen)

	OFFSET	`0,1`
	COMMENT	`Not equal to exp(-4/9), which agrees with the first 16 decimal places. Related to Jacobi theta constant theta_2 and Dedekind's eta(x^2)^2/eta(x): Sum_{n>=0} x^(n*(n+1)/2) = 1.9873697... (A106334). This constant divided by constant A106334 equals constant A106335, the radius of convergence of the g.f. of A106336.`
	FORMULA	`Sum_{n>=0} (1 - n(n+1)/2)x^(n*(n+1)/2) = 0.`
	EXAMPLE	`0 = 1 - 2x^3 - 5x^6 - 9x^10 - 14x^15 - 20x^21 - 27x^28 - ...` `x=0.641180388429954579645644888628301106553419618910071190877560305051317278`
	PROGRAM	`(PARI) solve(x=.6, .7, sum(n=0, 100, (1-n(n+1)/2)x^(n*(n+1)/2)))`
	CROSSREFS	`Cf. A106334, A106335, A106332, A106336.` `Adjacent sequences: A106330 A106331 A106332 this_sequence A106334 A106335 A106336` `Sequence in context: A097047 A021160 A060780 this_sequence A104748 A117335 A021863`
	KEYWORD	`cons,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Apr 29 2005`

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Last modified October 6 16:13 EDT 2008. Contains 144667 sequences.

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