A046224 Distinct numbers seen when writing first numerator and then denominator of central elements of 1/2-Pascal triangle.

1, 2, 3, 11, 40, 147, 546, 2046, 7722, 29315, 111826, 428298, 1646008, 6344366, 24515700, 94942620, 368404110, 1431985635, 5574725970, 21732560850, 84828633120, 331488081210, 1296712152060, 5077282282020, 19897457591700, 78039200913102, 306302623291476

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..200

Formula

a(n) = Sum_{k=1..n-2} (2*k+1)*binomial(2*n-k-5,n-3), n>2; a(1)=1, a(2)=2. - Vladimir Kruchinin, Sep 27 2011

a(n) = (5*n-9)/(8*n-12)*binomial(2*n-2,n-1), n>2; a(1)=1, a(2)=2. - Eric Werley, Sep 16 2015

G.f.: (3/2)*x^2 + (2*x - 3*x^2)/(2*sqrt(1-4*x)). - G. C. Greubel, Sep 24 2015

Example

1/1; <-- hence 1;
1/1 1/1;
1/1 1/2 1/1; <-- hence 2
1/1 3/2 3/2 1/1;
1/1 5/2 3/1 5/2 1/1; <-- hence 3
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; <-- hence 11
1/1 11/2 27/2 20/1 20/1 27/2 11/2 1/1;
...

Mathematica

Join[{1, 2}, Table[(5 n - 9)/(8 n - 12) Binomial[2 n - 2, n - 1], {n, 3, 40}]] (* Vincenzo Librandi, Sep 24 2015 *)

Prog

(Magma) [1, 2] cat [(5*n-9)/(8*n-12)*Binomial(2*n-2, n-1): n in [3..40]]; // Vincenzo Librandi, Sep 24 2015
(PARI) a(n) = if (n<3, n, (5*n-9)/(8*n-12)*binomial(2*n-2, n-1));
vector(40, n, a(n)) \\ Altug Alkan, Oct 01 2015

Crossrefs

Cf. A046213.

Sequence in context: A374312 A000280 A249402 * A081173 A179266 A265779

Adjacent sequences: A046221 A046222 A046223 * A046225 A046226 A046227

Keyword

nonn

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers, Dec 13 1999

a(26)-a(27) from Vincenzo Librandi, Sep 24 2015

Status

approved