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A120952 G.f. A(x) satisfies the condition that both series_reversion(x/A(x))/x (cf. A120953) and series_reversion(x*A(x))/x (cf. A120954) have zeros for every other coefficient after initial terms. 2
1, 1, 2, -7, -58, 369, 4572, -40188, -618694, 6915257, 123744242, -1683380975, -34017509348, 546799381140, 12298020900128, -228437416454904, -5666681561083638, 119532757362516473, 3247637352945151374, -76715605444589999941, -2268946268485834353378 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f. satisfies: A(x) = G(x/A(x)) where G(x) = g.f. of A120953. G.f. satisfies: A(x) = 1/H(x*A(x)) where H(x) = g.f. of A120954.

EXAMPLE

A(x) = 1 + x + 2*x^2 - 7*x^3 - 58*x^4 + 369*x^5 + 4572*x^6 --++...

series_reversion(x/A(x))/x = 1 + x + 3*x^2 - 65*x^4 + 4998*x^6 -+...

series_reversion(x*A(x))/x = 1 - x + 12*x^3 - 663*x^5 + 70992*x^7 -+...

PROG

(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, if(#A%2==1, A=concat(A, t); A[ #A]=-subst(Vec(serreverse(x/Ser(A)))[ #A], t, 0)); if(#A%2==0, A=concat(A, t); A[ #A]=subst(Vec(serreverse(x*Ser(A)))[ #A], t, 0))); A[n+1]}

CROSSREFS

Cf. A120953, A120954.

Sequence in context: A105183 A269994 A023364 * A270404 A270315 A083810

Adjacent sequences:  A120949 A120950 A120951 * A120953 A120954 A120955

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jul 19 2006

STATUS

approved

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Last modified February 29 08:26 EST 2020. Contains 332355 sequences. (Running on oeis4.)