A145158 - OEIS

%I #4 Aug 08 2014 15:30:14

%S 1,1,3,16,121,1143,12570,154551,2072547,29829412,455731327,7332989616,

%T 123548350018,2169987439342,39595583375433,748541216196285,

%U 14628467191450947,294984129900772611,6128372452917891216

%N G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x).

%H Vaclav Kotesovec, <a href="/A145158/b145158.txt">Table of n, a(n) for n = 0..160</a>

%F G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^2.

%F Self-convolution yields A145159.

%e G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 121*x^4 + 1143*x^5 +...

%e x/A(x)^2 = x - 2*x^2 - 3*x^3 - 18*x^4 - 150*x^5 - 1518*x^6 -...

%e 1/A(x) = 1 - x - 2*x^2 - 11*x^3 - 88*x^4 - 869*x^5 - 9876*x^6 -...

%e Series_Reversion[x/A(x)^2] = x + 2*x^2 + 11*x^3 + 88*x^4 + 869*x^5 +...

%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(n=0,n,B=serreverse(x/A^2);A=1/(1-B));polcoeff(A,n)}

%Y Cf. A145161 (A^3); A088713, A145160, A145162, A145165, A145167.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 03 2008