A046223 First denominator and then numerator of central elements of 1/2-Pascal triangle.

1, 1, 2, 1, 1, 3, 1, 11, 1, 40, 1, 147, 1, 546, 1, 2046, 1, 7722, 1, 29315, 1, 111826, 1, 428298, 1, 1646008, 1, 6344366, 1, 24515700, 1, 94942620, 1, 368404110, 1, 1431985635, 1, 5574725970, 1, 21732560850, 1, 84828633120, 1, 331488081210, 1

Offset

1,3

Comments

a(n) = A046222(n-1) for n > 5. - Georg Fischer, Oct 17 2018

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3000

Example

1/1; 1/1 1/1; 1/1 1/2 1/1; 1/1 3/2 3/2 1/1; 1/1 5/2 3/1 5/2 1/1; 1/1 7/2 11/2 11/2 7/2 1/1; 1/1 9/2 9/1 11/1 9/1 9/2 1/1; 1/1 11/2 27/2 20/1 20/1 27/2 11/2 1/1; ...

Mathematica

Map[{Denominator@ #, Numerator@ #} &@ #[[Ceiling[Length[#]/2] ]] &, Select[Nest[Append[#, Join[{#[[-1, 1]]}, Total /@ Partition[#[[-1]], 2, 1], {#[[-1, -1]]}]] &, {{1}, {1, 1}, {1, 1/2, 1}}, 2 (20) + 1], OddQ@ Length@ # & ]] // Flatten (* or *)
With[{r = Sqrt[1 - 4 x]}, {1, 1, 2, 1}~Join~Riffle[ConstantArray[1, Length@ #], #] &@ CoefficientList[Series[(2 - 2 r - 3 x - r x)/(2 r x^2), {x, 0, 19}], x]] (* Michael De Vlieger, Oct 17 2018 *)

Crossrefs

Cf. A046213, A046222.

Sequence in context: A104575 A318833 A173937 * A338398 A192181 A073463

Adjacent sequences: A046220 A046221 A046222 * A046224 A046225 A046226

Keyword

nonn

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers, Dec 13 1999

Status

approved