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 A146165 Expansion of q^(1/4) * eta(q^5)^2 * eta(q^20) / (eta(q^4) * eta(q^10)^2) in powers of q. 1

%I #5 Nov 25 2015 12:19:12

%S 1,0,0,0,1,-2,0,0,2,-2,1,0,3,-4,1,-2,5,-6,2,-2,10,-10,3,-4,14,-16,5,

%T -6,21,-24,11,-10,31,-34,15,-18,45,-50,23,-26,67,-70,34,-38,93,-104,

%U 50,-56,130,-140,77,-80,179,-196,107,-120,245,-264,151,-164,338,-360,210,-230,451,-488,290,-314,604,-650,404

%N Expansion of q^(1/4) * eta(q^5)^2 * eta(q^20) / (eta(q^4) * eta(q^10)^2) in powers of q.

%F Euler transform of period 20 sequence [ 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, ...].

%e q + q^17 - 2*q^21 + 2*q^33 - 2*q^37 + q^41 + 3*q^49 - 4*q^53 + q^57 + ...

%t QP = QPochhammer; s = QP[q^5]^2*(QP[q^20]/(QP[q^4]*QP[q^10]^2)) + O[q]^80; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 25 2015 *)

%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^5 + A)^2 * eta(x^20 + A) / (eta(x^4 + A) * eta(x^10 + A)^2), n))}

%Y Convolution inverse of A146164.

%K sign

%O 0,6

%A _Michael Somos_, Oct 27 2008

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Last modified August 13 00:55 EDT 2024. Contains 375113 sequences. (Running on oeis4.)