A288471 Exponents a(1), a(2), ... such that E_8, 1 + 480*q + 61920*q^2 + ... (A008410) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ... .

-480, 53520, -8192480, 1417877520, -261761532384, 50337746997520, -9956715872256480, 2010450258635669520, -412391756829925376480, 85648872592091236716816, -17967933476075186380800480, 3800832540589574135423637520

Offset: 1

Author

Seiichi Manyama, Jun 21 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..424

Crossrefs

Cf. A288968 (k=2), A110163 (k=4), A288851 (k=6), this sequence (k=8), A289024 (k=10), A288990/A288989 (k=12), A289029 (k=14).

Cf. A008410 (E_8), A008683, A288261 (E_10/E_8), A289638.

Formula

a(n) = 16 + (2/(3*n)) * Sum_{d|n} A008683(n/d) * A288261(d).

a(n) = 2 * A110163(n) = 2 * A013953(n^2). - Seiichi Manyama, Jun 22 2017

a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289638(d). - Seiichi Manyama, Jul 09 2017

a(n) ~ 2 * (-1)^n * exp(Pi*sqrt(3)*n) / n. - Vaclav Kotesovec, Mar 08 2018