A081205 Staircase on Pascal's triangle.

1, 3, 10, 20, 70, 126, 462, 792, 3003, 5005, 19448, 31824, 125970, 203490, 817190, 1307504, 5311735, 8436285, 34597290, 54627300, 225792840, 354817320, 1476337800, 2310789600, 9669554100, 15084504396, 63432274896, 98672427616

Offset: 0

Author

Paul Barry, Mar 11 2003

Keywords

• easy
• nonn

Comments

Arrange Pascal's triangle as a square array. A081204 is then a diagonal staircase on the square array. The steps are (1,3),(10,20),(70,126),(462,792),....

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A065942, A081181, A081204.

Programs

Magma

[Binomial(Ceiling((n+1)/2)+(n+1), n): n in [0..30]]; // Vincenzo Librandi Aug 07 2013

Mathematica

Table[Binomial[Ceiling[(n+1)/2] + (n + 1), n], {n, 0, 30}] (* Vincenzo Librandi, Aug 07 2013 *)

Formula

a(n) = binomial(ceiling((n+1)/2)+(n+1), n).

Conjecture: 4*n*(n-1)*(n+4)*(6*n^2-9*n-1)*a(n) +6*(n-1)*(27*n^2+29*n+4)*a(n-1) -3*n*(3*n-1)*(3*n+1)*(6*n^2+3*n-4)*a(n-2)=0. - R. J. Mathar, Nov 19 2014