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A282154 Coefficients in expansion of Eisenstein series -q*(d/dq)(q*(d/dq)E_2).

%I A282154 #20 Feb 27 2018 04:57:39
%S A282154 0,24,288,864,2688,3600,10368,9408,23040,25272,43200,34848,96768,
%T A282154 56784,112896,129600,190464,124848,303264,173280,403200,338688,418176,
%U A282154 304704,829440,465000,681408,699840,1053696,605520,1555200,738048,1548288,1254528,1498176
%N A282154 Coefficients in expansion of Eisenstein series -q*(d/dq)(q*(d/dq)E_2).
%H A282154 Seiichi Manyama, <a href="/A282154/b282154.txt">Table of n, a(n) for n = 0..1000</a>
%F A282154 -q*(d/dq)(q*(d/dq)E_2) = -q*(d/dq)((E_2^2 - E_4)/12) = -(E_2^3 - 3*E_2*E_4 + 2*E_6)/72.
%F A282154 a(n) = -(A282018(n) - 3*A282019(n) + 2*A013973(n))/72.
%F A282154 a(n) = 24*A282097(n).
%t A282154 terms = 35;
%t A282154 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A282154 -x*D[x*D[E2[x], x], x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)
%Y A282154 Cf. A006352 (E_2), A076835 (-q*(d/dq)E_2), this sequence (-q*(d/dq)(q*(d/dq)E_2)).
%Y A282154 Cf. A013973 (E_6), A282018 (E_2^3), A282019 (E_2*E_4), A282097.
%Y A282154 This sequence is related to A126858.
%K A282154 nonn
%O A282154 0,2
%A A282154 _Seiichi Manyama_, Feb 07 2017