OFFSET
0,2
FORMULA
a(n) = sum(j,0,n, C(n,j)*C(n-j,floor((n-j)/2))*A000108(floor((j+1)/2)) * A000108(ceiling((j+1)/2))), where C(n,j) = n!/(j!(n-j)!) and A000108(n) = Catalan(n).
Recurrence: (n+3)*(n+4)*(n+5)*(2*n+1)*(2*n+3)*a(n) = 8*(2*n+1)*(5*n^3 + 33*n^2 + 67*n + 45)*a(n-1) + 4*(n-1)*(40*n^4 + 216*n^3 + 326*n^2 + 144*n + 45)*a(n-2) - 288*(n-2)*(n-1)*(n+1)*(2*n+5)*a(n-3) - 144*(n-3)*(n-2)*(n-1)*(2*n+3)*(2*n+5)*a(n-4). - Vaclav Kotesovec, Feb 18 2015
a(n) ~ 6^(n+7/2) / (2 * Pi^(3/2) * n^(7/2)). - Vaclav Kotesovec, Feb 18 2015
MATHEMATICA
Array[Cat, 21, 0]; For[i = 0, i < 21, ++i, Cat[i] = (1/(i + 1))*Binomial[2*i, i]]; Table[Sum[ Binomial[n, j]*Binomial[n - j, Floor[(n - j)/2]]* Cat[Floor[(j + 1)/2]]*Cat[Ceiling[(j + 1)/2]], {j, 0, n}], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric S. Egge, Oct 22 2008
EXTENSIONS
More terms from Vaclav Kotesovec, Feb 18 2015
STATUS
approved