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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 July 21 14:09 EDT 2024. Contains 374474 sequences. (Running on oeis4.)