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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084772 Coefficients of 1/sqrt(1-12*x+16*x^2); also, a(n) is the central coefficient of (1+6x+5x^2)^n. 2
1, 6, 46, 396, 3606, 33876, 324556, 3151896, 30915046, 305543556, 3038019876, 30354866856, 304523343996, 3065412858696, 30946859111256, 313206733667376, 3176825392214406, 32284147284682596, 328643023505612596 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

H. A. Verrill, Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations, arXiv:math/0407327 [math.CO], 2008, Theorem 8.

FORMULA

a(n) = sum_{k=0..n} 5^k*C(n,k)^2. - Benoit Cloitre, Oct 26 2003

E.g.f.: exp(6*x)*BesselI(0, 2sqrt(5)*x). - Paul Barry, Sep 20 2004

Asymptotic: a(n) ~ (1+sqrt(5))^(2*n+1)/(2*5^(1/4)*sqrt(Pi*n)). - Vaclav Kotesovec, Sep 11 2012

n*a(n) +6*(1-2*n)*a(n-1) +16*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 09 2012

EXAMPLE

G.f.: 1/sqrt(1-2*b*x+(b^2-4*c)*x^2) yields central coefficients of (1+b*x+c*x^2)^n.

MATHEMATICA

Table[n! SeriesCoefficient[E^(6 x) BesselI[0, 2 Sqrt[5] x], {x, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, May 10 2013 *)

CoefficientList[Series[1/Sqrt[1-12x+16x^2], {x, 0, 30}], x] (* Harvey P. Dale, Apr 17 2015 *)

PROG

(PARI) for(n=0, 30, t=polcoeff((1+6*x+5*x^2)^n, n, x); print1(t", "))

CROSSREFS

Sequence in context: A253654 A288689 A271933 * A199563 A111531 A052781

Adjacent sequences:  A084769 A084770 A084771 * A084773 A084774 A084775

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 10 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 10:31 EDT 2017. Contains 292518 sequences.