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A303350
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Expansion of Product_{n>=1} (1 + 4*x^n)^(1/2).
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7
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1, 2, 0, 10, -10, 38, -76, 310, -960, 3190, -10672, 37262, -130170, 459690, -1639940, 5901498, -21376154, 77900710, -285457200, 1051118590, -3887169486, 14431323506, -53766825940, 200964040290, -753348868380, 2831669141514, -10670007388128
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OFFSET
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0,2
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COMMENTS
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This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/2, g(n) = -4.
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LINKS
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FORMULA
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a(n) ~ -(-1)^n * sqrt(c) * 2^(2*n - 1) / (sqrt(Pi) * n^(3/2)), where c = Product_{k>=2} (1 + 4*(-1/4)^k) = 1.1864623436704848646891654544376222586... - Vaclav Kotesovec, Apr 22 2018
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MAPLE
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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
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MATHEMATICA
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nmax = 30; CoefficientList[Series[Product[(1 + 4*x^k)^(1/2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+4*x^k)^(1/2)))
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CROSSREFS
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Expansion of Product_{n>=1} (1 + b^2*x^n)^(1/b): A000009 (b=1), this sequence (b=2), A303351 (b=3).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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