A134717 Odd Motzkin numbers.

1, 1, 9, 21, 51, 127, 323, 835, 15511, 41835, 853467, 2356779, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 208023278209, 593742784829, 1697385471211, 4859761676391, 13933569346707, 40002464776083, 953467954114363, 2750016719520991, 7939655757745265

Offset: 1

Author

Omar E. Pol, Nov 11 2007

Keywords

• easy
• nonn

Comments

A001006 except A134718. - Vladimir Reshetnikov, Nov 02 2015

The asymptotic density of this sequence within the Motzkin numbers is 2/3. - Amiram Eldar, Aug 26 2024

Links

• Robert Israel, Table of n, a(n) for n = 1..801

Crossrefs

Cf. A001006, A134718, A161674.

Programs

Maple

S:= series(exp(x)*BesselI(1, 2*x)/x, x, 500):
select(type, [seq(simplify(coeff(S,x,j)*j!), j=0..498)], odd); # Robert Israel, Nov 03 2015

Mathematica

Select[Table[(-1)^n Hypergeometric2F1[3/2, -n, 3, 4], {n, 0, 40}], OddQ] (* Vladimir Reshetnikov, Nov 02 2015 *)

PARI

a001006(n) = polcoeff((1-x-sqrt((1-x)^2-4*x^2+x^3*O(x^n)))/ (2*x^2), n); for(n=0, 100, if((m=a001006(n))%2==1, print1(m", "))) \\ Altug Alkan, Nov 03 2015

Formula

a(n) = A001006(A161674(n)). - Amiram Eldar, Aug 26 2024