OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ 5 * 2^(2*n+2) / (27 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2018
G.f.: (1 + x)*(1 - sqrt(1 - 4*x))/(2*(1 - x)^3). - Ilya Gutkovskiy, Mar 21 2018
MAPLE
a:= proc(n) option remember; `if`(n<3, n*(3*n-1)/2,
((60*n^3-232*n^2+264*n-90) *a(n-1)
-(90*n^3-308*n^2+257*n-24) *a(n-2)
+2*(2*n-3)*(10*n^2-12*n+1) *a(n-3))/ (n*(10*n^2-32*n+23)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 10 2013
MATHEMATICA
a[n_] := Sum[CatalanNumber[k]*(k-n)^2, {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 16 2017 *)
PROG
(PARI) a(n) = sum(i=0, n, i^2*(2*(n-i))!/((n-i)!*(n-i+1)!)); \\ Michel Marcus, Nov 10 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved