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

Author

Mohammad K. Azarian

Keywords

• nonn

Examples

			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;
...
		

Links

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

Crossrefs

Cf. A046213.

Programs

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

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 *)

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

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

Extensions

More terms from James Sellers, Dec 13 1999

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