A157108 Triangle, read by rows, T(n, k) = binomial(n*binomial(n, k), k).

1, 1, 1, 1, 4, 1, 1, 9, 36, 1, 1, 16, 276, 560, 1, 1, 25, 1225, 19600, 12650, 1, 1, 36, 4005, 280840, 2555190, 376992, 1, 1, 49, 10731, 2421090, 146475945, 534017484, 13983816, 1, 1, 64, 24976, 14885696, 4053946260, 147055790784, 163995687856, 621216192, 1

Offset

0,5

Comments

Row sums are: {1, 2, 6, 47, 854, 33502, 3217065, 696909117, 315741551830, 339451781249846, 856885032450030756, ...}.

Links

G. C. Greubel, Rows n = 0..50 of triangle, flattened

Formula

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

Example

Triangle begins as:
  1;
  1,  1;
  1,  4,     1;
  1,  9,    36,       1;
  1, 16,   276,     560,         1;
  1, 25,  1225,   19600,     12650,         1;
  1, 36,  4005,  280840,   2555190,    376992,        1;
  1, 49, 10731, 2421090, 146475945, 534017484, 13983816, 1;

Maple

seq(seq( binomial(n*binomial(n, k), k), k=0..n), n=0..10); # G. C. Greubel, Nov 30 2019

Mathematica

Table[Binomial[n*Binomial[n, k], k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(PARI) T(n, k) = binomial(n*binomial(n, k), k); \\ G. C. Greubel, Nov 30 2019
(Magma) [Binomial(n*Binomial(n, k), k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 30 2019
(Sage) [[binomial(n*binomial(n, k), k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 30 2019
(GAP) Flat(List([0..10], n-> List([0..n], k-> Binomial(n*Binomial(n, k), k) ))); # G. C. Greubel, Nov 30 2019

Crossrefs

Sequence in context: A126062 A243608 A219207 * A376553 A056647 A056057

Adjacent sequences: A157105 A157106 A157107 * A157109 A157110 A157111

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 23 2009

Status

approved