OFFSET
1,1
COMMENTS
a(n) = Sum_{k=1..n} k*A121445(n,k).
FORMULA
a(n)=3n(23n^2+78n+67)binomial(3n+2,n+2)/[4(n+3)(2n+1)(2n+3)(2n+5)].
G.f.= (h-1-z)(h-1)/z^2, where h=1+zh^3=2sin(arcsin(sqrt(27z/4))/3)/sqrt(3z).
D-finite with recurrence -2*(2*n+5)*(n+3)*(1951*n-2094)*a(n) +(43553*n^3+142716*n^2+115045*n-10338)*a(n-1) +3*(2281*n+1723)*(3*n-1)*(3*n-2)*a(n-2)=0. - R. J. Mathar, Jul 24 2022
EXAMPLE
a(1)=3 because each of the trees /, | and \ contributes 1 to the sum.
MAPLE
a:=n->3*n*(23*n^2+78*n+67)*binomial(3*n+2, n+2)/4/(n+3)/(2*n+1)/(2*n+3)/(2*n+5): seq(a(n), n=1..23);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jul 30 2006
STATUS
approved