A098173 Triangle T(n,k) with diagonals T(n,n-k) = binomial(n, 4k).

1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 5, 1, 0, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 0, 0, 35, 1, 0, 0, 0, 0, 0, 0, 1, 70, 1, 0, 0, 0, 0, 0, 0, 0, 9, 126, 1, 0, 0, 0, 0, 0, 0, 0, 0, 45, 210, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 165, 330, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 495, 495, 1

Offset: 0

Author

Paul Barry, Aug 30 2004

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A038503.

Examples

			Rows begin
  {1},
  {0,1},
  {0,0,1},
  {0,0,0,1},
  {0,0,0,1,1},
  {0,0,0,0,5,1},
  ...
		

Links

• Seiichi Manyama, Rows n = 0..139, flattened

Crossrefs

Cf. A098158, A098172.

Programs

GAP

Flat(List([0..12], n-> List([0..n], k-> Binomial(n, 4*(n-k)) ))); # G. C. Greubel, Mar 15 2019

Magma

[[Binomial(n, 4*(n-k)): k in [0..n]]: n in [0..12]]; // G. C. Greubel, Mar 15 2019

Mathematica

Table[Binomial[n, 4(n-k)], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 15 2019 *)

PARI

{T(n, k) = binomial(n, 4*(n-k))}; \\ G. C. Greubel, Mar 15 2019

Sage

[[binomial(n, 4*(n-k)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 15 2019

Formula

Triangle T(n, k) = binomial(n, 4(n-k)).