OFFSET
0,2
COMMENTS
Arrange Pascal's triangle as a square array. a(n) is then a diagonal staircase on the square array. A companion staircase is given by A065942.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
a(n) = binomial(floor((n + 1)/2) + (n + 1), n).
Conjecture: 8*n*(n+3)*(1845*n-2882)*a(n) +4*(-5097*n^3+11143*n^2 +42110*n-27416)*a(n-1) +6*(-16605*n^3-7272*n^2-16701*n+9490)*a(n-2) +3*(3*n-5)*(5097*n-949)*(3*n-4)*a(n-3)=0. - R. J. Mathar, Oct 29 2014
MATHEMATICA
Table[Binomial[Floor[(n + 1) / 2] + (n + 1), n], {n, 0, 30}] (* Vincenzo Librandi, Aug 06 2013 *)
PROG
(Magma) [Binomial(Floor((n+1)/2)+(n+1), n): n in [0..30]]; // Vincenzo Librandi, Aug 06 2013
(SageMath) [binomial(((n+1)//2)+(n+1), n) for n in range(41)] # G. C. Greubel, Jan 14 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved