cp's OEIS Frontend

A272461 G.f. A(x) satisfies: A( x - A(x^4)/x^2 ) = x.

%I A272461 #9 May 03 2016 05:07:47
%S A272461 1,1,2,5,14,43,140,474,1650,5865,21194,77623,287492,1074915,4051824,
%T A272461 15381073,58749102,225621404,870686810,3374625925,13130575110,
%U A272461 51271434788,200845390668,789081913225,3108496250028,12275905239752,48590260462470,192736593501813,766007363990640,3049978926971396,12164745517874576,48596364360237882,194426663474794450,778968350863994065
%N A272461 G.f. A(x) satisfies: A( x - A(x^4)/x^2 ) = x.
%H A272461 Paul D. Hanna, <a href="/A272461/b272461.txt">Table of n, a(n) for n = 1..300</a>
%F A272461 a(n) ~ c * d^n / n^(3/2), where d = 4.1920029654932692520828... and c = 0.1046247209912855075794... . - _Vaclav Kotesovec_, May 03 2016
%e A272461 G.f.: A(x) = x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 140*x^7 + 474*x^8 + 1650*x^9 + 5865*x^10 + 21194*x^11 + 77623*x^12 +...
%e A272461 where A( x - A(x^4)/x^2 ) = x.
%e A272461 RELATED SERIES.
%e A272461 Let B(x) be the series reversion of the g.f. A(x) so that A(B(x)) = x, then
%e A272461 B(x) = x - x^2 - x^6 - 2*x^10 - 5*x^14 - 14*x^18 - 43*x^22 - 140*x^26 - 474*x^30 - 1650*x^34 - 5865*x^38 - 21194*x^42 - 77623*x^46 +...
%e A272461 such that B(x) = x - A(x^4)/x^2.
%o A272461 (PARI) {a(n) = my(A=x); for(i=1,n, A = serreverse( x - subst(A,x,x^4 +x^3*O(x^n))/x^2 )); polcoeff(A,n)}
%o A272461 for(n=1,50,print1(a(n),", "))
%Y A272461 Cf. A141200, A272460.
%K A272461 nonn
%O A272461 1,3
%A A272461 _Paul D. Hanna_, Apr 29 2016