|
| |
| |
|
|
|
1, 11, 136, 1787, 24376, 341048, 4859968, 70223483, 1025790616, 15116164136, 224365547968, 3350371999928, 50287277411008, 758124098549696, 11473331826459136, 174221578556572283, 2653437885092286808, 40520013896165905928
(list; graph; refs; listen; history; 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 (v.reshetnikov(AT)gmail.com), Jan 20, 2011.
|
|
|
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: A015609 A157773 A024143 * A123800 A142895 A201111
Adjacent sequences: A057715 A057716 A057717 * A057719 A057720 A057721
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 23 2000
|
| |
|
|
