A157109 Triangle, read by rows, T(n, k) = binomial(n*binomial(n, floor((n-k)/2)), k).

1, 1, 1, 1, 2, 1, 1, 9, 3, 1, 1, 16, 120, 4, 1, 1, 50, 300, 2300, 5, 1, 1, 90, 4005, 7140, 58905, 6, 1, 1, 245, 10731, 518665, 211876, 1906884, 7, 1, 1, 448, 100128, 1848224, 102114376, 7624512, 74974368, 8, 1, 1, 1134, 285390, 71728020, 450710001, 28845440064, 324540216, 3477216600, 9, 1

Offset

0,5

Comments

Row sums are: {1, 2, 4, 14, 142, 2657, 70148, 2648410, 186662066, 33169921436, 11592123179902, ...}.

Links

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

Formula

T(n, k) = binomial(n*binomial(n, floor((n-k)/2)), k).

Example

Triangle begins as:
  1;
  1,   1;
  1,   2,      1;
  1,   9,      3,       1;
  1,  16,    120,       4,         1;
  1,  50,    300,    2300,         5,       1;
  1,  90,   4005,    7140,     58905,       6,        1;
  1, 245,  10731,  518665,    211876, 1906884,        7, 1;
  1, 448, 100128, 1848224, 102114376, 7624512, 74974368, 8, 1;

Maple

seq(seq( binomial(n*binomial(n, floor((n-k)/2)), k), k=0..n), n=0..10); # G. C. Greubel, Nov 30 2019

Mathematica

Table[Binomial[n*Binomial[n, Floor[(n-m)/2]], m], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(PARI) T(n, k) = binomial(n*binomial(n, (n-k)\2), k); \\ G. C. Greubel, Nov 30 2019
(Magma) [Binomial(n*Binomial(n, Floor((n-k)/2)), k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 30 2019
(Sage) [[binomial(n*binomial(n, floor((n-k)/2)), 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, Int((n-k)/2)), k) ))); # G. C. Greubel, Nov 30 2019

Crossrefs

Sequence in context: A144946 A332717 A260374 * A185814 A174553 A167015

Adjacent sequences: A157106 A157107 A157108 * A157110 A157111 A157112

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 23 2009

Status

approved