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A046223 First denominator and then numerator of central elements of 1/2-Pascal triangle. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 20:20 EDT 2021. Contains 348070 sequences. (Running on oeis4.)