cp's OEIS Frontend

A211855 G.f. satisfies: A(x) = (1+x*A(x)^3)*(1+x^2*A(x)^2)*(1+x^3*A(x)).

%I A211855 #6 Nov 22 2017 07:42:57
%S A211855 1,1,4,19,98,553,3288,20287,128681,833889,5496837,36742204,248454438,
%T A211855 1696588460,11682677436,81031854579,565614332353,3970182041035,
%U A211855 28006229772030,198438070511163,1411652452459443,10078529348799106,72192155099054325,518659038159324250
%N A211855 G.f. satisfies: A(x) = (1+x*A(x)^3)*(1+x^2*A(x)^2)*(1+x^3*A(x)).
%H A211855 Vaclav Kotesovec, <a href="/A211855/b211855.txt">Table of n, a(n) for n = 0..500</a>
%F A211855 a(n) ~ sqrt(s*(2*r*s + s^2 + 5*r^4*s^2 + 4*r^3*s^3 + 6*r^5*s^5 + 3*r^2*(1 + s^4)) / (Pi*(r + 3*s + 3*r^4*s + 6*r^3*s^2 + 10*r^2*s^3 + 15*r^5*s^4))) / (2*n^(3/2)*r^n), where r = 0.1303652752058746790368151406944165350206179676971... and s = 1.504659035764367744283558911063644754705733371817... are real roots of the system of equations (1 + r^3*s)*(1 + r^2*s^2)*(1 + r*s^3) = s, r*(2*r*s + 3*s^2 + 3*r^4*s^2 + 4*r^3*s^3 + 6*r^5*s^5 + r^2*(1 + 5*s^4)) = 1. - _Vaclav Kotesovec_, Nov 22 2017
%e A211855 G.f.: A(x) = 1 + x + 4*x^2 + 19*x^3 + 98*x^4 + 553*x^5 + 3288*x^6 +...
%e A211855 Related expansions:
%e A211855 A(x)^2 = 1 + 2*x + 9*x^2 + 46*x^3 + 250*x^4 + 1454*x^5 + 8827*x^6 +...
%e A211855 A(x)^3 = 1 + 3*x + 15*x^2 + 82*x^3 + 468*x^4 + 2808*x^5 + 17431*x^6 +...
%e A211855 A(x)^4 = 1 + 4*x + 22*x^2 + 128*x^3 + 765*x^4 + 4736*x^5 + 30086*x^6 +...
%e A211855 A(x)^5 = 1 + 5*x + 30*x^2 + 185*x^3 + 1155*x^4 + 7376*x^5 + 47970*x^6 +...
%e A211855 A(x)^6 = 1 + 6*x + 39*x^2 + 254*x^3 + 1653*x^4 + 10884*x^5 + 72474*x^6 +...
%e A211855 where A(x) = 1 + x*A(x)^3 + x^2*A(x)^2 + x^3*(A(x)+A(x)^5) + x^4*A(x)^4 + x^5*A(x)^3 + x^6*A(x)^6.
%o A211855 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=(1+x*A^3)*(1+x^2*A^2)*(1+x^3*A)+x*O(x^n)); polcoeff(A, n)}
%o A211855 for(n=0, 40, print1(a(n), ", "))
%Y A211855 Cf. A182053, A211854.
%K A211855 nonn
%O A211855 0,3
%A A211855 _Paul D. Hanna_, Apr 22 2012