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
Seiichi Manyama, Table of n, a(n) for n = 0..1000
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 22 2018
STATUS
approved