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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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 23 2000
STATUS
approved

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)