login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304940 Expansion of ((1 + 4*x)/(1 - 4*x))^(1/2). 2
1, 4, 8, 32, 96, 384, 1280, 5120, 17920, 71680, 258048, 1032192, 3784704, 15138816, 56229888, 224919552, 843448320, 3373793280, 12745441280, 50981765120, 193730707456, 774922829824, 2958796259328, 11835185037312, 45368209309696, 181472837238784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let ((1 + k*x)/(1 - k*x))^(m/k) = a(0) + a(1)*x + a(2)*x^2 + ...

Then n*a(n) = 2*m*a(n-1) + k^2*(n-2)*a(n-2) for n > 1.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

n*a(n) = 4*a(n-1) + 4^2*(n-2)*a(n-2) for n > 1.

a(n) = 2^n * A063886(n).

PROG

(PARI) N=66; x='x+O('x^N); Vec(((1+4*x)/(1-4*x))^(1/2))

CROSSREFS

((1 + 4*x)/(1 - 4*x))^(m/4): A303537 (m=1), this sequence (m=2), A304941 (m=3), A081654 (m=4).

Cf. A063886.

Sequence in context: A086344 A209084 A254216 * A068205 A241684 A254878

Adjacent sequences:  A304937 A304938 A304939 * A304941 A304942 A304943

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 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 August 15 01:28 EDT 2020. Contains 336484 sequences. (Running on oeis4.)