login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157108 Triangle, read by rows, T(n, k) = binomial(n*binomial(n, k), k). 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A056647 A056057 A226234

Adjacent sequences:  A157105 A157106 A157107 * A157109 A157110 A157111

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 23 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 23 21:20 EST 2020. Contains 332195 sequences. (Running on oeis4.)