A134717 - OEIS

%I #19 Aug 26 2024 04:58:26

%S 1,1,9,21,51,127,323,835,15511,41835,853467,2356779,50852019,

%T 142547559,400763223,1129760415,3192727797,9043402501,208023278209,

%U 593742784829,1697385471211,4859761676391,13933569346707,40002464776083,953467954114363,2750016719520991,7939655757745265

%N Odd Motzkin numbers.

%C A001006 except A134718. - _Vladimir Reshetnikov_, Nov 02 2015

%C The asymptotic density of this sequence within the Motzkin numbers is 2/3. - _Amiram Eldar_, Aug 26 2024

%H Robert Israel, <a href="/A134717/b134717.txt">Table of n, a(n) for n = 1..801</a>

%F a(n) = A001006(A161674(n)). - _Amiram Eldar_, Aug 26 2024

%p S:= series(exp(x)*BesselI(1, 2*x)/x, x, 500):

%p select(type, [seq(simplify(coeff(S,x,j)*j!), j=0..498)], odd); # _Robert Israel_, Nov 03 2015

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

%o (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

%Y Cf. A001006, A134718, A161674.

%K easy,nonn

%O 1,3

%A _Omar E. Pol_, Nov 11 2007