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A305443 Expansion of q * f(-q^1, -q^6)^3 / f(-q^2, -q^5)^2 * f(-q^3, -q^4) in powers of q where f() is Ramanujan's two-variable theta function. 3

%I #71 Oct 19 2018 09:21:19

%S 1,-3,5,-6,7,-7,3,4,-12,22,-32,35,-28,13,14,-53,90,-116,126,-105,42,

%T 53,-164,280,-366,378,-301,128,142,-469,773,-978,1015,-805,322,374,

%U -1179,1942,-2450,2492,-1946,791,884,-2809,4558,-5678,5754,-4473,1781,2004,-6251,10104

%N Expansion of q * f(-q^1, -q^6)^3 / f(-q^2, -q^5)^2 * f(-q^3, -q^4) in powers of q where f() is Ramanujan's two-variable theta function.

%H Seiichi Manyama, <a href="/A305443/b305443.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>

%t nmax = 50; CoefficientList[Series[Product[((1 - x^(7*k - 1)) * (1 - x^(7*k - 6)))^3 / ((1 - x^(7*k - 2))^2 * (1 - x^(7*k - 5))^2 * (1 - x^(7*k - 3)) * (1 - x^(7*k - 4))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 11 2018 *)

%Y Convolution inverse of A108481.

%Y Cf. A262933.

%K sign

%O 1,2

%A _Seiichi Manyama_, Oct 10 2018

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Last modified April 23 11:04 EDT 2024. Contains 371905 sequences. (Running on oeis4.)