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A303350
Expansion of Product_{n>=1} (1 + 4*x^n)^(1/2).
7
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
OFFSET
0,2
COMMENTS
This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -1/2, g(n) = -4.
LINKS
FORMULA
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
MAPLE
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
MATHEMATICA
nmax = 30; CoefficientList[Series[Product[(1 + 4*x^k)^(1/2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+4*x^k)^(1/2)))
CROSSREFS
Expansion of Product_{n>=1} (1 + b^2*x^n)^(1/b): A000009 (b=1), this sequence (b=2), A303351 (b=3).
Sequence in context: A362994 A371551 A334615 * A351879 A070681 A228539
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 22 2018
STATUS
approved