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!)
A085458 a(0)=1, for n>0: a(n)=4 Sum(C(2i+1,i)C(n-1,n-1-i)(-1)^(n-1-i)2^i,(i=0,..,n-1)). 1
1, 4, 20, 116, 708, 4452, 28532, 185300, 1215268, 8030404, 53381844, 356577588, 2391430020, 16092704292, 108605848116, 734783381652, 4982063186916, 33844621986180, 230306722637204, 1569571734301172, 10711405584991300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: sqrt((1+x)/(1-7*x))

7^n = sum(i=0..n, sum(j=0..i, (-1)^(n-i)*a(j)*a(i-j) )).

Recurrence: n*a(n) = 2*(3*n-1)*a(n-1) + 7*(n-2)*a(n-2). - Vaclav Kotesovec, Oct 14 2012

a(n) ~ 2*sqrt(2)*7^(n-1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 14 2012

MATHEMATICA

CoefficientList[Series[Sqrt[(1 + x)/(1 - 7x)], {x, 0, 25}], x]

PROG

(PARI) x='x+O('x^66); Vec(sqrt((1+x)/(1-7*x))) \\ Joerg Arndt, May 10 2013

CROSSREFS

Sequence in context: A231539 A106567 A077445 * A085456 A120915 A165311

Adjacent sequences:  A085455 A085456 A085457 * A085459 A085460 A085461

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Jul 02 2003

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 21 14:18 EDT 2021. Contains 348155 sequences. (Running on oeis4.)