Search: id:A139380
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%I A139380
%S A139380 1,2,0,0,2,0,0,0,0,0,4,0,0,4,0,0,2,0,0,8,0,0,8,0,0,2,0,0,16,0,0,16,0,0,
%T A139380 4,0,0,28,0,0,28,0,0,8,0,0,48,0,0,46,0,0,12,0,0,80,0,0,76,0,0,20,0,0,
%U A139380 126,0,0,120,0,0,32,0,0,196,0,0,184,0,0,48,0,0,300,0,0,280,0,0,72,0,0
%V A139380 1,2,0,0,2,0,0,0,0,0,-4,0,0,-4,0,0,2,0,0,8,0,0,8,0,0,-2,0,0,-16,0,0,-16,
               0,0,4,0,0,28,0,
%W A139380 0,28,0,0,-8,0,0,-48,0,0,-46,0,0,12,0,0,80,0,0,76,0,0,-20,0,0,-126,0,0,
               -120,0,0,32,0,0,
%X A139380 196,0,0,184,0,0,-48,0,0,-300,0,0,-280,0,0,72,0,0
%N A139380 Expansion of phi(q) / phi(q^9) in powers of q where phi() is a Ramanujan 
               theta function.
%F A139380 Expansion of 1 + 2 * q * chi(q^3) / chi(q^9)^3 in powers of q where chi() 
               is a Ramanujan theta function.
%F A139380 Expansion of 1 - 2 * c(q^6) / c(-q^3) in powers of q where c() is a cubic 
               AGM function.
%F A139380 Expansion of eta(q^2)^5 * eta(q^9)^2 * eta(q^36)^2 / (eta(q)^2 * eta(q^4)^2 
               * eta(q^18)^5) in powers of q.
%F A139380 Euler transform of period 36 sequence [ 2, -3, 2, -1, 2, -3, 2, -1, 0, 
               -3, 2, -1, 2, -3, 2, -1, 2, 0, 2, -1, 2, -3, 2, -1, 2, -3, 0, -1, 
               2, -3, 2, -1, 2, -3, 2, 0, ...].
%F A139380 G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^3 - u 
               * (3 - u) * (v - 1) * (3 - 2*u + u*v).
%F A139380 G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 3 
               / f(t) where q = exp(2 pi i t).
%F A139380 a(3*n) = 0 unless n=0. a(3*n + 2) = 0.
%F A139380 G.f.: (1 + 2 * Sum_{k>0} x^k^2) / (1 + 2 * Sum_{k>0} x^(9*k^2)).
%F A139380 G.f.: Product_{k>0} (1 - x^(2*k)) * (1 + x^(2*k-1))^2 / ((1 - x^(18*k)) 
               * (1 + x^(18*k-9))^2).
%F A139380 A128771(n) = (-1)^n * a(n). 2 * A128111(n) = a(3*n + 1).
%e A139380 1 + 2*q + 2*q^4 - 4*q^10 - 4*q^13 + 2*q^16 + 8*q^19 + 8*q^22 - 2*q^25 
               + ...
%o A139380 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 
               + A)^5 * eta(x^9 + A)^2 * eta(x^36 + A)^2 / (eta(x + A)^2 * eta(x^4 
               + A)^2 * eta(x^18 + A)^5), n))}
%Y A139380 Sequence in context: A109983 A093492 A128771 this_sequence A000122 A002448 
               A033759
%Y A139380 Adjacent sequences: A139377 A139378 A139379 this_sequence A139381 A139382 
               A139383
%K A139380 sign
%O A139380 0,2
%A A139380 Michael Somos, Apr 15 2008

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