A272460 - OEIS

%I #8 May 03 2016 04:56:30

%S 1,1,2,5,15,49,168,596,2170,8063,30451,116545,451038,1762065,6939684,

%T 27523374,109832228,440668881,1776599145,7193526536,29240389629,

%U 119276102017,488106369196,2003299984825,8244088853598,34010402405020,140627814353509,582704045483909,2419228983607503,10062353339406026,41924039720446064,174952464642171681,731184941189099208,3060168941260579386

%N G.f. A(x) satisfies: A( x - A(x^3)/x ) = x.

%H Paul D. Hanna, <a href="/A272460/b272460.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) ~ c * d^n / n^(3/2), where d = 4.3788729685558146277374586... and c = 0.0933818743555997288781743... . - _Vaclav Kotesovec_, May 03 2016

%e G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 49*x^6 + 168*x^7 + 596*x^8 + 2170*x^9 + 8063*x^10 + 30451*x^11 + 116545*x^12 +...

%e where A( x - A(x^3)/x ) = x.

%e RELATED SERIES.

%e Let B(x) be the series reversion of g.f. A(x), A(B(x)) = x, then

%e B(x) = x - x^2 - x^5 - 2*x^8 - 5*x^11 - 15*x^14 - 49*x^17 - 168*x^20 - 596*x^23 - 2170*x^26 - 8063*x^29 - 30451*x^32 - 116545*x^35 +...

%e such that B(x) = x - A(x^3)/x.

%o (PARI) {a(n) = my(A=x); for(i=1,n, A = serreverse( x - subst(A,x,x^3 +x^3*O(x^n))/x )); polcoeff(A,n)}

%o for(n=1,50,print1(a(n),", "))

%Y Cf. A141200, A272461.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Apr 29 2016