A289029 Exponents a(1), a(2), ... such that E_14, 1 - 24*q - 196632*q^2 + ... (A058550) is equal to (1-q)^a(1) (1-q^2)^a(2) (1-q^3)^a(3) ... .

24, 196908, 42987544, 21974456220, 8544538312728, 3980088408377644, 1793770730037338136, 847156322106368439324, 401870774532436947447832, 193962999708079363021283628, 94363580764388112933729226776, 46332621615483591171320408201116

Offset

1,1

Comments

This sequence is related to the identity: E_4^2*E_6 = E_4*E_10 = E_6*E_8 = E_14.

Links

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

Formula

a(n) = 2 * A110163(n) + A288851(n) = A110163(n) + A289024(n) = A288851(n) + A288471(n) = 28 + (1/n) * (Sum_{d|n} A008683(n/d) * (2/3 * A288261(d) + 1/2 * A288840(d))).

a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289640(d). - Seiichi Manyama, Jul 09 2017

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

Crossrefs

Cf. A288968 (k=2), A110163 (k=4), A288851 (k=6), A288471 (k=8), A289024 (k=10), A288990/A288989 (k=12), this sequence (k=14).

Cf. A008683, A288261 (E_6/E_4), A288840 (E_8/E_6), A289640.

Sequence in context: A058550 A145200 A007240 * A287964 A173172 A061526

Adjacent sequences: A289026 A289027 A289028 * A289030 A289031 A289032

Keyword

nonn

Author

Seiichi Manyama, Jun 22 2017

Status

approved