A289024 Exponents a(1), a(2), ... such that E_10, 1 - 264*q - 135432*q^2 + ... (A013974) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ... .

264, 170148, 47083784, 21265517460, 8675419078920, 3954919534878884, 1798749087973466376, 846151096977050604564, 402076970410851910136072, 193920175271783317402925220, 94372564731126150526919627016, 46330721199213296384252696382356

Offset: 1

Author

Seiichi Manyama, Jun 22 2017

Keywords

• nonn

Comments

This sequence is related to the identity: E_4*E_6 = E_10.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..367

Crossrefs

Cf. A288968 (k=2), A110163 (k=4), A288851 (k=6), A288471 (k=8), this sequence (k=10), A288990/A288989 (k=12), A289029 (k=14).

Cf. A008683, A288261 (E_6/E_4), A288840 (E_8/E_6), A289639.

Formula

a(n) = A110163(n) + A288851(n) = 20 + (1/n) * (Sum_{d|n} A008683(n/d) * (1/3 * A288261(d) + 1/2 * A288840(d))).

a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289639(d). - Seiichi Manyama, Jul 09 2017

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