A288968 Exponents a(1), a(2), ... such that E_2, 1 - 24*q - 72*q^2 - ... (A006352) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ... .

24, 348, 6424, 129300, 2778648, 62114524, 1428337176, 33527349924, 799482197272, 19302454317660, 470740035601176, 11575875047000596, 286650683468840472, 7140515309818664028, 178783562850377621272, 4496350112540599930692

Offset: 1

Author

Seiichi Manyama, Jun 20 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..701

Crossrefs

Cf. this sequence (k=2), A110163 (k=4), A288851 (k=6), A288471 (k=8), A289024 (k=10), A288990/A288989 (k=12), A289029 (k=14).

Cf. A006352 (E_2), A008683, A288877 (E_4/E_2), A289635.

Formula

a(n) = 2 + (1/(12*n)) * Sum_{d|n} A008683(n/d) * A288877(d).

a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289635(d).

a(n) ~ 1 / (n * r^(2*n)), where r = A057823. - Vaclav Kotesovec, Mar 08 2018