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A282154 Coefficients in expansion of Eisenstein series -q*(d/dq)(q*(d/dq)E_2). 2
0, 24, 288, 864, 2688, 3600, 10368, 9408, 23040, 25272, 43200, 34848, 96768, 56784, 112896, 129600, 190464, 124848, 303264, 173280, 403200, 338688, 418176, 304704, 829440, 465000, 681408, 699840, 1053696, 605520, 1555200, 738048, 1548288, 1254528, 1498176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

-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.

a(n) = -(A282018(n) - 3*A282019(n) + 2*A013973(n))/72.

a(n) = 24*A282097(n).

MATHEMATICA

terms = 35;

E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];

-x*D[x*D[E2[x], x], x] + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 27 2018 *)

CROSSREFS

Cf. A006352 (E_2), A076835 (-q*(d/dq)E_2), this sequence (-q*(d/dq)(q*(d/dq)E_2)).

Cf. A013973 (E_6), A282018 (E_2^3), A282019 (E_2*E_4), A282097.

This sequence is related to A126858.

Sequence in context: A001496 A055754 A297082 * A035707 A035475 A288458

Adjacent sequences:  A282151 A282152 A282153 * A282155 A282156 A282157

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 07 2017

STATUS

approved

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Last modified September 23 08:18 EDT 2020. Contains 337295 sequences. (Running on oeis4.)