Search: id:A027364
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%I A027364
%S A027364 1,216,3348,13888,52110,723168,2822456,4078080,3139803,11255760,20586852,
               46497024,
%T A027364 190073338,609650496,174464280,1335947264,1646527986,678197448,1563257180,
%U A027364 723703680,9449582688,4446760032,9451116072,13653411840,27802126025,41055841008
%V A027364 1,216,-3348,13888,52110,-723168,2822456,-4078080,-3139803,11255760,20586852,
               -46497024,
%W A027364 -190073338,609650496,-174464280,-1335947264,1646527986,-678197448,1563257180,
%X A027364 723703680,-9449582688,4446760032,9451116072,13653411840,-27802126025,
               -41055841008
%N A027364 Coefficients of unique normalized cusp form Delta_16 of weight 16 for 
               full modular group.
%D A027364 H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for 
               coefficients of modular forms, pp. 1-55 of Modular Functions of One 
               Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.
%H A027364 S. R. Finch, <A HREF="http://algo.inria.fr/bsolve/">Modular forms on 
               SL_2(Z)</A>
%H A027364 <a href="Sindx_Gre.html#groups_modular">Index entries for sequences related 
               to modular groups</a>
%H A027364 Author?, <a href="http://www.math.okstate.edu/~loriw/degree2/degree2hm/
               level1/weight16/c16.html">Table of coefficients c16(n) of the weight 
               16 cusp form on Gamma_0(1) for n up to 1000</a>
%H A027364 F. Q. Gouvea, <a href="http://www.expmath.org/restricted/6/6.3/gouvea.ps">
               Non-ordinary primes</a>, Experimental Mathematics 6 195, 1997.
%F A027364 G.f.: q (1+240 Sum sigma_3(n)q^n; n=1..inf) Product (1-q^k)^24; k=1..inf. 
               sigma_3(n) is the sum of the cubes of the divisors of n (A001158).
%F A027364 (E_4^4-E_6^2*E_4)/1728.
%e A027364 q^2+216*q^4-3348*q^6+13888*q^8+...
%p A027364 with(numtheory): DO := qs -> q*diff(qs,q)/2: E2:=1-24*add(sigma(n)*q^(2*n),
               n=1..100): delta16:=(-1/24)*(DO@@6)(E2)*E2+(9/8)*(DO@@5)(E2)*(DO@@1)(E2)-(45/
               8)*(DO@@4)(E2)*(DO@@2)(E2)+(55/12)*(DO@@3)(E2)*(DO@@3)(E2):seq(coeff(delta16,
               q,2*i),i=1..40); with(numtheory): E2n:=n->1-(4*n/bernoulli(2*n))*add(sigma[2*n-1](k)*q^(2*k),
               k=1..100): qs:=(E2n(2)^4-E2n(3)^2*E2n(2))/1728: seq(coeff(qs,q,2*i),
               i=1..40); (Ronaldo)
%Y A027364 Cf. A000594 (cusp form of weight 12).
%Y A027364 Sequence in context: A016911 A017055 A017139 this_sequence A017235 A152241 
               A017343
%Y A027364 Adjacent sequences: A027361 A027362 A027363 this_sequence A027365 A027366 
               A027367
%K A027364 sign,easy
%O A027364 1,2
%A A027364 Paolo Dominici (pl.dm(AT)libero.it), N. J. A. Sloane (njas(AT)research.att.com).
%E A027364 More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005

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