OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..260
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
(1) 2 = Sum_{n=-oo..+oo} x^n * (1 + x^n)^n * (1+x)^(n^2) * A(x)^n.
(2) 2 = Sum_{n=-oo..+oo} x^(n*(n-1)) * (1+x)^(n^2) / ((1 + x^n)^n * A(x)^n).
EXAMPLE
G.f.: A(x) = 1 + x + 6*x^2 + 29*x^3 + 148*x^4 + 865*x^5 + 5481*x^6 + 35891*x^7 + 240290*x^8 + 1642093*x^9 + 11426333*x^10 + 80724482*x^11 + 577729923*x^12 + ...
PROG
(PARI) {a(n) = my(V=[1], A=1); for(i=1, n, V=concat(V, 0); A=Ser(V);
V[#V] = polcoef( sum(m=-#V, #V, x^m*(1 + x^m +x*O(x^#V))^m*(1+x +x*O(x^#V))^(m^2) * A^m), #V-1)); V[n+1]}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 15 2025
STATUS
approved