A081181 Staircase on Pascal's triangle.

1, 3, 6, 20, 35, 126, 210, 792, 1287, 5005, 8008, 31824, 50388, 203490, 319770, 1307504, 2042975, 8436285, 13123110, 54627300, 84672315, 354817320, 548354040, 2310789600, 3562467300, 15084504396, 23206929840, 98672427616, 151532656696

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

Cf. A065942.

Sequence in context: A359963 A276748 A339639 * A062164 A265112 A052408

Adjacent sequences: A081178 A081179 A081180 * A081182 A081183 A081184

Keyword

easy,nonn

Author

Paul Barry, Mar 11 2003

Status

approved