A292811 - OEIS

%I #4 Sep 23 2017 23:30:50

%S 2,3,-6,21,-72,96,1740,-22914,153162,-282138,-6414408,71836596,

%T -70221204,-5275053936,29070675696,561036692121,-6339036232368,

%U -82893851049960,1603373884497120,14900133962766312,-462354052414272480,-3413078936604832032,157313543770476035136,1032487368620917863024,-63597712357849352307264,-419977031579672070661344,30319524013631926908243168,227333388435264016786353072

%N G.f.: A(x) satisfies: A( A(x) - x ) = 2*x + 9*x^2.

%H Paul D. Hanna, <a href="/A292811/b292811.txt">Table of n, a(n) for n = 1..300</a>

%e G.f.: A(x) = 2*x + 3*x^2 - 6*x^3 + 21*x^4 - 72*x^5 + 96*x^6 + 1740*x^7 - 22914*x^8 + 153162*x^9 - 282138*x^10 - 6414408*x^11 + 71836596*x^12 - 70221204*x^13 - 5275053936*x^14 +...

%e such that A( A(x) - x ) = 2*x + 9*x^2.

%o (PARI) {a(n) = my(A=x, V=[2, 3]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(G=A, x, A - x) )[#V]/(-3) ); V[n]}

%o for(n=1,30,print1(a(n),", "))

%Y Cf. A291198, A292812, A292813, A292814.

%K sign

%O 1,1

%A _Paul D. Hanna_, Sep 23 2017