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A303347 Expansion of Product_{n>=1} (1 - 4*x^n)^(1/2). 3

%I #18 Apr 25 2018 04:00:30

%S 1,-2,-4,-2,-6,-6,-56,-158,-612,-2070,-7228,-25238,-89646,-319466,

%T -1150168,-4164978,-15177718,-55592614,-204617788,-756314982,

%U -2806456898,-10450497682,-39040372248,-146273912858,-549533738952,-2069680656234,-7812908945556

%N Expansion of Product_{n>=1} (1 - 4*x^n)^(1/2).

%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/2, g(n) = 4.

%H Seiichi Manyama, <a href="/A303347/b303347.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ -c * 2^(2*n-1) / (sqrt(Pi) * n^(3/2)), where c = QPochhammer[1/4]^(1/2) = 0.8297816201389011939293261374110190... - _Vaclav Kotesovec_, Apr 25 2018

%p seq(coeff(series(mul((1-4*x^k)^(1/2), k = 1..n), x, n+1), x, n), n=0..40); # _Muniru A Asiru_, Apr 22 2018

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-4*x^k)^(1/2)))

%Y Expansion of Product_{n>=1} (1 - b^2*x^n)^(1/b): A010815 (b=1), this sequence (b=2), A303348 (b=3).

%Y Cf. A067855, A303350.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 22 2018

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)