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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) ... .
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%I #22 Mar 08 2018 06:41:09

%S 24,196908,42987544,21974456220,8544538312728,3980088408377644,

%T 1793770730037338136,847156322106368439324,401870774532436947447832,

%U 193962999708079363021283628,94363580764388112933729226776,46332621615483591171320408201116

%N 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) ... .

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

%H Seiichi Manyama, <a href="/A289029/b289029.txt">Table of n, a(n) for n = 1..367</a>

%F 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))).

%F a(n) = (1/n) * Sum_{d|n} A008683(n/d) * A289640(d). - _Seiichi Manyama_, Jul 09 2017

%F a(n) ~ exp(2*Pi*n) / n. - _Vaclav Kotesovec_, Mar 08 2018

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

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

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jun 22 2017