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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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) ~ -(-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).

Cf. A261568, A303347, A303352.

Sequence in context: A002741 A213322 A151887 * A070681 A228539 A061189

Adjacent sequences:  A303347 A303348 A303349 * A303351 A303352 A303353

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 October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)