login
A303347
Expansion of Product_{n>=1} (1 - 4*x^n)^(1/2).
3
1, -2, -4, -2, -6, -6, -56, -158, -612, -2070, -7228, -25238, -89646, -319466, -1150168, -4164978, -15177718, -55592614, -204617788, -756314982, -2806456898, -10450497682, -39040372248, -146273912858, -549533738952, -2069680656234, -7812908945556
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) ~ -c * 2^(2*n-1) / (sqrt(Pi) * n^(3/2)), where c = QPochhammer[1/4]^(1/2) = 0.8297816201389011939293261374110190... - Vaclav Kotesovec, Apr 25 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
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): A010815 (b=1), this sequence (b=2), A303348 (b=3).
Sequence in context: A198540 A216369 A083791 * A325971 A250222 A026251
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 22 2018
STATUS
approved