OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
(1) 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(3*n-1).
(2) 1 = Sum_{n=-oo..+oo} (-1)^(n+1) * x^(3*n^2) / (1 - 2*A(x)*(-x)^n)^(3*n+1).
EXAMPLE
G.f.: A(x) = 1 + 2*x + 34*x^2 + 677*x^3 + 15660*x^4 + 393790*x^5 + 10433402*x^6 + 286990626*x^7 + 8117763488*x^8 + 234635708480*x^9 + 6899771599141*x^10 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=-#A, #A, x^m * (2*Ser(A) - (-x)^m)^(3*m-1) ), #A-1)/2); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 13 2023
STATUS
approved