A386669 G.f. Sum_{n=-oo..+oo} x^n * (1 + x^n)^(n^3).

2, 0, 3, 0, 10, 0, 57, 0, 122, 351, 197, 0, 5215, 0, 374, 25300, 42178, 0, 104718, 0, 954008, 354663, 1663, 0, 10300656, 9691375, 3915, 2485431, 81640573, 0, 327928582, 0, 643447570, 9321400, 24363, 5257311235, 8244703613, 0, 57249, 19796166, 110277192614

Offset

0,1

Comments

It appears that for n > 1, a(n) = 0 iff n is an odd prime.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Formula

G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.

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

(2) A(x) = Sum_{n=-oo..+oo} x^(n^4-n) / (1 + x^n)^(n^3).

Example

G.f.: A(x) = 2 + 3*x^2 + 10*x^4 + 57*x^6 + 122*x^8 + 351*x^9 + 197*x^10 + 5215*x^12 + 374*x^14 + 25300*x^15 + 42178*x^16 + ...

Prog

(PARI) {a(n) = my(A = sum(m=-n-1, n+1, x^m * (1 + x^m +x*O(x^n))^(m^3) ) ); polcoef(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Sequence in context: A308218 A067165 A079981 * A117776 A298610 A186492

Adjacent sequences: A386666 A386667 A386668 * A386670 A386671 A386672

Keyword

nonn

Author

Paul D. Hanna, Sep 19 2025

Status

approved