A288968 - OEIS

%I #30 Mar 08 2018 06:22:42

%S 24,348,6424,129300,2778648,62114524,1428337176,33527349924,

%T 799482197272,19302454317660,470740035601176,11575875047000596,

%U 286650683468840472,7140515309818664028,178783562850377621272,4496350112540599930692

%N 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) ... .

%H Seiichi Manyama, <a href="/A288968/b288968.txt">Table of n, a(n) for n = 1..701</a>

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

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

%F a(n) ~ 1 / (n * r^(2*n)), where r = A057823. - _Vaclav Kotesovec_, Mar 08 2018

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

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

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jun 20 2017