A157113 Triangle, read by rows, T(n,k) = binomial(n*(n-k)*k, k) + binomial(n*(n-k)*k, n -k).

2, 1, 1, 1, 4, 1, 1, 21, 21, 1, 1, 232, 240, 232, 1, 1, 4865, 4495, 4495, 4865, 1, 1, 142536, 195708, 49608, 195708, 142536, 1, 1, 5245828, 12105429, 2024785, 2024785, 12105429, 5245828, 1, 1, 231917456, 927052864, 190858864, 21336000, 190858864, 927052864, 231917456, 1

Offset

0,1

Comments

Row sums are: {2, 2, 6, 44, 706, 18722, 726098, 38752086, 2720994370, 241584879476, 26221233537242, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n,k) = binomial(n*(n-k)*k, k) + binomial(n*(n-k)*k, n-k).

Example

Triangle begins as:
  2;
  1,       1;
  1,       4,        1;
  1,      21,       21,       1;
  1,     232,      240,     232,       1;
  1,    4865,     4495,    4495,    4865,        1;
  1,  142536,   195708,   49608,  195708,   142536,       1;
  1, 5245828, 12105429, 2024785, 2024785, 12105429, 5245828, 1;

Maple

b:=binomial; seq(seq( b(n*(n-k)*k, k) + b(n*(n-k)*k, n-k), k=0..n), n=0..10); # G. C. Greubel, Nov 29 2019

Mathematica

Table[Binomial[n*(n-k)*k, k] + Binomial[n*(n-k)*k, n-k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(PARI) my(b=binomial); T(n, k) = b(n*(n-k)*k, k) + b(n*(n-k)*k, n-k); \\ G. C. Greubel, Nov 29 2019
(Magma) B:=Binomial; [B(n*(n-k)*k, k) + B(n*(n-k)*k, n-k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 29 2019
(Sage) b=binomial; [[b(n*(n-k)*k, k) + b(n*(n-k)*k, n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 29 2019
(GAP) B:=Binomial;; Flat(List([0..10], n-> List([0..n], k-> B(n*(n-k)*k, k) + B(n*(n-k)*k, n-k) ))); # G. C. Greubel, Nov 29 2019

Crossrefs

Sequence in context: A156786 A156141 A174555 * A214712 A213330 A139320

Adjacent sequences: A157110 A157111 A157112 * A157114 A157115 A157116

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 23 2009

Status

approved