OFFSET
0,4
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies:
(1) x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(n*(n+1)) * A(x)^(n^2).
(2) -x = Product_{n>=1} (1 - x^(2*n)*A(x)^(2*n-1)) * (1 - x^(2*n-2)*A(x)^(2*n-1)) * (1 - x^(2*n)*A(x)^(2*n)), due to the Jacobi triple product identity.
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^(m-1) * x^(m*(m+1)) * Ser(A)^(m^2) ), #A-1)); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 17 2023
STATUS
approved