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

1,3

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A001006, A134718, A161674.

Sequence in context: A251212 A176896 A347502 * A216980 A372664 A147169

Adjacent sequences: A134714 A134715 A134716 * A134718 A134719 A134720

Keyword

easy,nonn

Author

Omar E. Pol, Nov 11 2007

Status

approved