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%I #8 Sep 08 2022 08:46:11
%S 1,-5,8,-2,-5,4,-11,19,-2,-6,-9,-7,26,-2,-7,-4,-6,11,-5,-7,12,12,4,
%T -32,-20,28,23,1,0,-52,24,7,5,12,-10,-8,-11,12,-1,33,-28,-2,-32,22,12,
%U 9,26,-26,-40,-19,33,44,-8,18,-33,-32,34,-44,8,58,16,-66,7,-13
%N Expansion of cusp form for Gamma1(11) of weight 3 in powers of q with expansion being q^5 + ...
%H G. C. Greubel, <a href="/A256453/b256453.txt">Table of n, a(n) for n = 5..1000</a>
%F Euler transform of period 11 sequence [-5, -2, -2, -1, 1, 1, -1, -2, -2, -5, -6, ...].
%e G.f. = q^5 - 5*q^6 + 8*q^7 - 2*q^8 - 5*q^9 + 4*q^10 - 11*q^11 + 19*q^12 + ...
%t a[ n_] := SeriesCoefficient[ q^5 Product[(1 - q^k)^{5, 2, 2, 1, -1, -1, 1, 2, 2, 5, 6}[[Mod[k, 11, 1]]], {k, 1, n - 5}], {q, 0, n}];
%o (PARI) {a(n) = my(A); if( n<5, 0, n -= 5; A = 1 + x * O(x^n); polcoeff( prod(k=1, n, (1 - x^k)^[6, 5, 2, 2, 1, -1, -1, 1, 2, 2, 5][k%11 + 1], A), n))};
%o (Magma) Basis( CuspForms( Gamma1(11), 3), 69) [5];
%K sign
%O 5,2
%A _Michael Somos_, Mar 29 2015
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