0,2

a(n) = T(2n,2n) = coefficient of x^(2n) in (1+x+x^2)^(2n), T is the trinomial triangle A027907; Integral representation : a(n) = 1/Pi Integral[(1+2x)^(2n)/Sqrt[1-x^2],{x,-1, 1}], i.e. a(n) is the moment of order 2n of the random variable 1+2X, where the distribution of X is an arcsin law on the interval (-1,1). - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Jan 22 2008

a(n) = Sum[ T(n, k)^2, {k, 0, n} ] where T(n, k) = trinomial coefficients (A027907).

a(n)=sum(k=0, n, binomial(2*n-k, k)*binomial(2*n, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 30 2003

G.f.: (1/sqrt(1+2x-3x^2)+1/sqrt(1-2x-3x^2))/2 (with interpolated zeros) - Paul Barry (pbarry(AT)wit.ie), Jan 04 2005

a(n)=sum{k=0..n, C(2n,2k)*C(2k,k)}=sum{k=0..n, C(n+k,2k)*C(2n,n+k)}; [From Paul Barry (pbarry(AT)wit.ie), Dec 16 2008]

(PARI) a(n)=sum(k=0, n, binomial(2*n-k, k)*binomial(2*n, k))

Bisection of A002426.

Sequence in context: A074559 A027314 A025571 this_sequence A110525 A058859 A095002

Adjacent sequences: A082755 A082756 A082757 this_sequence A082759 A082760 A082761

easy,nonn

Emanuele Munarini (munarini(AT)mate.polimi.it), May 21 2003