This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341801 #9 Feb 22 2021 09:17:58
%S A341801 1,-24,-13932,-3585216,-1580941068,-628142318640,-281617154080704,
%T A341801 -126114490533924480,-58596395743623957084,-27537281150571923942424,
%U A341801 -13153668428658997172513880,-6345860505664230715931502912,-3091029995619009106117946403456
%N A341801 Coefficients of the series whose 12th power equals E_2*E_4*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973.
%C A341801 The g.f. is the 12th root of the g.f. of A282102.
%C A341801 It is easy to see that E_2(x)*E_4(x)*E_6(x) == 1 - 24*Sum_{k >= 1} (k - 10*k^3 + 21*k*5)*x^k/(1 - x^k) (mod 72), and also that the integer k - 10*k^3 + 21*k*5 = k*(3*k^2 - 1)*(7^k^2 - 1) is always divisible by 3. Hence, E_2(x)*E_4(x)*E_6(x) == 1 (mod 72). It follows from Heninger et al., p. 3, Corollary 2, that the series expansion of (E_2(x)*E_4(x)* E_6(x))^(1/12) = 1 - 24*x - 13932*x^2 - 3585216*x^3 - 1580941068*x^4 - ... has integer coefficients.
%H A341801 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%H A341801 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_series">Eisenstein series</a>
%p A341801 E(2,x) := 1 - 24*add(k*x^k/(1-x^k), k = 1..20):
%p A341801 E(4,x) := 1 + 240*add(k^3*x^k/(1-x^k), k = 1..20):
%p A341801 E(6,x) := 1 - 504*add(k^5*x^k/(1-x^k), k = 1..20):
%p A341801 with(gfun): series((E(2,x)*E(4,x)*E(6,x))^(1/12), x, 20):
%p A341801 seriestolist(%);
%Y A341801 Cf. A004009, A006352, A013973, A108091, A109817, A282102, A289392.
%K A341801 sign,easy
%O A341801 0,2
%A A341801 _Peter Bala_, Feb 20 2021