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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057718 A036917/8 (omitting leading term of A036917). 1
1, 11, 136, 1787, 24376, 341048, 4859968, 70223483, 1025790616, 15116164136, 224365547968, 3350371999928, 50287277411008, 758124098549696, 11473331826459136, 174221578556572283, 2653437885092286808, 40520013896165905928 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that a(n) == 16^n/Pi^3 * Integrate[x=0..1, x^n*F(x)*F(1-x)], where F(x) = Pi/2 * hypergeometric([1/2, 1/2], [1], x) (== elliptic K(sqrt(x))). - Vladimir Reshetnikov, Jan 20 2011

LINKS

Table of n, a(n) for n=1..18.

FORMULA

G.f.: 7/8 + (1/2)*(K(16x)/pi)^2, where K(x) is the elliptic integral of the first kind (as defined in Mathematica). - Emanuele Munarini, Mar 12 2011

a(n) = (1/8)*sum(binomial(2k,k)^2*binomial(2n-2k,n-k)^2, k=0..n) for n >= 1. - Emanuele Munarini, Mar 12 2011

MAPLE

seq(add(binomial(2*k, k)^2*binomial(2*(n-k), n-k)^2, k=0..n)/8, n=1..12); # Emanuele Munarini, Mar 12 2011

MATHEMATICA

Table[Sum[Binomial[2k, k]^2 Binomial[2n-2k, n-k]^2, {k, 0, n}]/8, {n, 1, 12}] (* Emanuele Munarini, Mar 12 2011 *)

PROG

(Maxima) makelist(sum(binomial(2*k, k)^2*binomial(2*(n-k), n-k)^2, k, 0, n)/8, n, 1, 12); /* Emanuele Munarini, Mar 12 2011 */

CROSSREFS

Sequence in context: A209487 A227101 A024143 * A123800 A233258 A262382

Adjacent sequences:  A057715 A057716 A057717 * A057719 A057720 A057721

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 23 2000

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 June 27 19:44 EDT 2017. Contains 288790 sequences.