%I #44 Feb 27 2018 11:59:11
%S 1,-528,-4284,147712,-1025850,2261952,3225992,-8785920,-110787507,
%T 541648800,-753618228,-632798208,2541064526,-1703323776,4394741400,
%U -14721941504,-5429742318,58495803696,1487499860,-151530355200
%N Coefficients of unique normalized cusp form Delta_18 of weight 18 for full modular group.
%H Seiichi Manyama, <a href="/A037944/b037944.txt">Table of n, a(n) for n = 1..1000</a>
%H Steven R. Finch, <a href="/A000521/a000521_1.pdf">Modular forms on SL_2(Z)</a>, December 28, 2005. [Cached copy, with permission of the author]
%H Fernando Q. GouvĂȘa, <a href="http://projecteuclid.org/euclid.em/1047920420">Non-ordinary primes: a story</a>, Experimental Mathematics, Volume 6, Issue 3 (1997), 195-205.
%H S. C. Milne, <a href="https://arxiv.org/abs/math/0009130">Hankel determinants of Eisenstein series</a>, preprint, arXiv:0009130 [math.NT], 2000.
%H H. P. F. Swinnerton-Dyer, <a href="http://dx.doi.org/10.1007/978-3-540-37802-0_1">On l-adic representations and congruences for coefficients of modular forms</a>, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.
%H <a href="/index/Gre#groups_modular">Index entries for sequences related to modular groups</a>
%F Convolution product of A000594 and A013973. - _Michael Somos_, Mar 18 2012
%F a(n) == A013965(n) mod 43867. - _Seiichi Manyama_, Feb 02 2017
%F G.f.: 691/(1728*250) * (E_4(q)*E_14(q) - E_6(q)*E_12(q)). - _Seiichi Manyama_, Jul 25 2017
%e G.f. = q - 528*q^2 - 4284*q^3 + 147712*q^4 - 1025850*q^5 + 2261952*q^6 + ...
%t terms = 20;
%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];
%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];
%t E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];
%t E14[x_] = 1 - 24*Sum[k^13*x^k/(1 - x^k), {k, 1, terms}];
%t (691/(1728*250))*(E4[x]*E14[x] - E6[x]*E12[x]) + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* _Jean-François Alcover_, Feb 27 2018, after _Seiichi Manyama_ *)
%o (PARI) {a(n) = if( n<0, 0, polcoeff( x * eta(x + x * O(x^n))^24 * (1 - 504 * sum( k=1, n, sigma( k, 5) * x^k)), n))}; /* _Michael Somos_, Mar 18 2012 */
%Y Cf. A000594, A013965, A013973, A027364, A037945, A037946, A037947, A290048.
%K sign
%O 1,2
%A _N. J. A. Sloane_