A119574 a(n) = binomial(2*n,n)*(n+2)^2/(n+1).

4, 9, 32, 125, 504, 2058, 8448, 34749, 143000, 588302, 2418624, 9934834, 40770352, 167152500, 684656640, 2801810205, 11455885080, 46801769190, 191055480000, 779363066790, 3177034283280, 12942655253580, 52693956656640, 214412258531250, 871975203591024

Offset: 0

Author

Zerinvary Lajos, May 31 2006

Keywords

• easy
• nonn

Links

• Sela Fried, On the generating function of A119574, 2024.

Crossrefs

Cf. A000108, A000290, A000984, A037965, A110609.

Programs

Maple

[seq (binomial(2*n,n)*(n+2)^2/(n+1),n=0..25)];

Mathematica

Table[Binomial[2n,n] (n+2)^2/(n+1),{n,0,30}] (* Harvey P. Dale, Jun 02 2024 *)

Formula

Conjectured g.f.: (-1 + 14*x - 36*x^2 + (1 - 4*x)^(3/2))/(2*x*(1 - 4*x)^(3/2)). - Harvey P. Dale, Jun 02 2024.

The conjecture is true (see links). - Sela Fried, Oct 02 2024.

a(n) = A000108(n)*A000290(n+2). - Alois P. Heinz, Oct 02 2024