A281374 - OEIS

%I #15 Feb 23 2018 03:40:25

%S 1,-48,432,3264,9456,21600,39744,66432,105840,147984,220320,281664,

%T 393792,475104,646272,743040,980592,1091232,1432944,1536960,1965600,

%U 2118144,2649024,2761344,3516480,3557040,4433184,4594560,5575296,5603040,6998400,6864384,8407152,8494848,10085472,9918720,12319152

%N Coefficients in q-expansion of E_2^2, where E_2 is the Eisenstein series shown in A006352.

%H Seiichi Manyama, <a href="/A281374/b281374.txt">Table of n, a(n) for n = 0..1000</a>

%p with(numtheory); M:=100;

%p E := proc(k) local n, t1; global M;

%p t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);

%p series(t1, q, M+1); end;

%p e2:=E(2); e4:=E(4); e6:=E(6);

%p series(e2^2,q,M+1);

%p seriestolist(%);

%t terms = 37;

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

%t E2[x]^2 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 23 2018 *)

%Y Cf. A006352.

%K sign

%O 0,2

%A _N. J. A. Sloane_, Feb 05 2017