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A081205
Staircase on Pascal's triangle.
2
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
0,2
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
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
MATHEMATICA
Table[Binomial[Ceiling[(n+1)/2] + (n + 1), n], {n, 0, 30}] (* Vincenzo Librandi, Aug 07 2013 *)
PROG
(Magma) [Binomial(Ceiling((n+1)/2)+(n+1), n): n in [0..30]]; // Vincenzo Librandi Aug 07 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved