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A366733
Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (3 - x^(n-1))^(n+1).
6
1, 3, 12, 90, 702, 5838, 50895, 458103, 4225683, 39745665, 379730658, 3674980518, 35951809104, 354950991006, 3532167377340, 35390917028619, 356742401734236, 3615164398809324, 36809446799831823, 376387507560832992, 3863438843523528636, 39794189982905311407
OFFSET
0,2
COMMENTS
a(n) = Sum_{k=0..n} A366730(n,k) * 3^k for n >= 0.
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) ).
EXAMPLE
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 + ...
PROG
(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), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 29 2023
STATUS
approved