A366733 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (3 - x^(n-1))^(n+1).

1, 3, 12, 90, 702, 5838, 50895, 458103, 4225683, 39745665, 379730658, 3674980518, 35951809104, 354950991006, 3532167377340, 35390917028619, 356742401734236, 3615164398809324, 36809446799831823, 376387507560832992, 3863438843523528636, 39794189982905311407

Offset: 0

Author

Paul D. Hanna, Oct 29 2023

Keywords

• nonn

Comments

a(n) = Sum_{k=0..n} A366730(n,k) * 3^k for n >= 0.

Examples

			G.f.: A(x) = 1 + 3*x + 12*x^2 + 90*x^3 + 702*x^4 + 5838*x^5 + 50895*x^6 + 458103*x^7 + 4225683*x^8 + 39745665*x^9 + 379730658*x^10 + ...
		

Crossrefs

Cf. A366730, A366731, A366732, A366734, 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 * (3 - 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 * (3 - x^(n-1))^(n+1).

(2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 - 3*x^(n+1))^(n-1) ).