A155927 - OEIS

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A155927

G.f. satisfies: A(x) = B(x/A(x)) where A(x) = Sum_{n>=0} a(n)*x^n/[n!*(n+1)!/2^n] and B(x) = A(x*B(x)) = Sum_{n>=0} x^n/[n!*(n+1)!/2^n].

1, 1, -2, 19, -379, 12726, -641465, 45181627, -4232016719, 508271819428, -76108505872794, 13896010073569130, -3038043685025188631, 783439451518414509612, -235289860249420249309140 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	FORMULA	`G.f. satisfies: A(x) = F(x/A(x)^2) and F(x) = A(xF(x)^2) where F(x) = Sum_{n>=0} A155926(n)x^n/[n!(n+1)!/2^n].` `G.f. satisfies: A(x) = 1/G(x/A(x)) and G(x) = 1/A(x/G(x)) where G(x) = Sum_{n>=0} A103365(n)x^n/[n!*(n+1)!/2^n].`
	EXAMPLE	`G.f.: A(x) = 1 + x - 2x^2/3 + 19x^3/18 - 379x^4/180 + 12726x^5/2700 +...+ a(n)x^n/[n!(n+1)!/2^n] +...` `G.f. satisfies: A(x) = B(x/A(x)) and B(x) = A(xB(x)) where:` `B(x) = 1 + x + 1/3x^2 + 1/18x^3 + 1/180x^4 +...+ x^n/[n!(n+1)!/2^n] +...` `G.f. satisfies: A(x) = F(x/A(x)^2) and F(x) = A(xF(x)^2) where:` `F(x) = 1 + x + 4x^2/3 + 37x^3/18 + 621x^4/180 + 16526x^5/2700 +...+ A155926(n)x^(n+1)/[n!(n+1)!/2^n] +...` `G.f. satisfies: A(x) = 1/G(x/A(x)) and G(x) = 1/A(x/G(x)) where:` `G(x) = 1 - x + 2x^2/3 - 7x^3/18 + 39x^4/180 - 321x^5/2700 +...+ A103365(n)x^(n+1)/[n!(n+1)!/2^n] +...`
	PROG	`(PARI) {a(n)=local(B=sum(k=0, n, x^k/(k!(k+1)!/2^k))+xO(x^n)); polcoeff(x/serreverse(xB), n)n!*(n+1)!/2^n}`
	CROSSREFS	`Cf. A155926, A103365.` `Sequence in context: A078369 A090308 A110818 * A120420 A158099 A015204` `Adjacent sequences: A155924 A155925 A155926 * A155928 A155929 A155930`
	KEYWORD	`sign`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Jan 31 2009`

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Last modified February 16 11:30 EST 2012. Contains 205907 sequences.