A361775 - OEIS

%I #13 Aug 05 2023 14:29:23

%S 1,1,5,21,95,405,1680,6926,28257,115254,471785,1908622,7444553,

%T 27617809,101165030,411727344,1980777419,9377434309,30465401498,

%U 5465053256,-319249451709,3800908753389,79369582680985,507720631888326,-779604798853789,-39876367011094054

%N Expansion of g.f. A(x) satisfying x = Sum_{n=-oo..+oo} (-1)^n * x^n * A(x)^n * (A(x)^n + x^n)^n.

%H Paul D. Hanna, <a href="/A361775/b361775.txt">Table of n, a(n) for n = 0..201</a>

%F G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.

%F (1) x = Sum_{n=-oo..+oo} (-1)^n * (x*A(x))^n * (A(x)^n + x^n)^n.

%F (2) x = Sum_{n=-oo..+oo} (-1)^n * (x*A(x))^(n*(n-1)) / (A(x)^n + x^n)^n.

%e G.f.: A(x) = 1 + x + 5*x^2 + 21*x^3 + 95*x^4 + 405*x^5 + 1680*x^6 + 6926*x^7 + 28257*x^8 + 115254*x^9 + 471785*x^10 + ...

%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);

%o A[#A] = polcoeff(x - sum(m=-#A,#A, (-1)^m * x^m * Ser(A)^m * (Ser(A)^m + x^m)^m ),#A-1));A[n+1]}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A361776, A292088.

%K sign

%O 0,3

%A _Paul D. Hanna_, May 08 2023