OFFSET
0,2
FORMULA
a(n) = sum(M(i),i=n..2*n), where the M(n)'s are the Motzkin numbers.
Recurrence: a(n+1) = a(n) + M(2n+2) + M(2n+1) - M(n).
MATHEMATICA
M[n_]:=If[n==0, 1, Coefficient[(1+x+x^2)^(n+1), x^n]/(n+1)]; Table[Sum[M[i], {i, n, 2n}], {n, 0, 40}]
PROG
(Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)), x^n)/(n+1);
makelist(sum(M(i), i, n, 2*n), n, 0, 20);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Apr 06 2012
STATUS
approved