A366734 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).

1, 4, 24, 236, 2504, 28332, 335656, 4108688, 51558000, 659737684, 8575826448, 112927383328, 1503232394344, 20195196226124, 273467339844368, 3728623506924660, 51145851271818536, 705322823588365592, 9772995790887474920, 135992755093954566300, 1899633478390401668072

Offset: 0

Author

Paul D. Hanna, Oct 29 2023

Keywords

• nonn

Comments

a(n) = Sum_{k=0..n} A366730(n,k) * 4^k for n >= 0.

Examples

			G.f.: A(x) = 1 + 4*x + 24*x^2 + 236*x^3 + 2504*x^4 + 28332*x^5 + 335656*x^6 + 4108688*x^7 + 51558000*x^8 + 659737684*x^9 + 8575826448*x^10 + ...
		

Crossrefs

Cf. A366730, A366731, A366732, A366733, A366735.

Programs

PARI

{a(n) = my(A=[1]); for(i=1,n, A = concat(A,0);
A[#A] = polcoeff( sum(n=-#A,#A, x^n * Ser(A)^n * (4 - x^(n-1))^(n+1) ), #A-2));A[n+1]}
for(n=0,30,print1(a(n),", "))

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.

(1) 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).

(2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 - 4*x^(n+1))^(n-1) ).