login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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) ~ -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).

Cf. A067855, A303350.

Sequence in context: A198540 A216369 A083791 * A250222 A026251 A205721

Adjacent sequences:  A303344 A303345 A303346 * A303348 A303349 A303350

KEYWORD

sign

AUTHOR

Seiichi Manyama, Apr 22 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)