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A321716 Triangle read by rows: T(n,k) is the number of n X k Young tableaux, where 0 <= k <= n. 2
1, 1, 1, 1, 1, 2, 1, 1, 5, 42, 1, 1, 14, 462, 24024, 1, 1, 42, 6006, 1662804, 701149020, 1, 1, 132, 87516, 140229804, 396499770810, 1671643033734960, 1, 1, 429, 1385670, 13672405890, 278607172289160, 9490348077234178440, 475073684264389879228560 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Seiichi Manyama, Rows n = 0..30, flattened

Wikipedia, Hook length formula

Index entries for sequences related to Young tableaux.

FORMULA

T(n,k) = (n*k)! / (Product_{i=1..n} Product_{j=1..k} (i+j-1)).

T(n,k) = A060854(n,k) for n,k > 0.

EXAMPLE

T(4,3) = 12! / ((6*5*4)*(5*4*3)*(4*3*2)*(3*2*1)) = 462.

Triangle begins:

1;

1, 1;

1, 1,   2;

1, 1,   5,    42;

1, 1,  14,   462,     24024;

1, 1,  42,  6006,   1662804,    701149020;

1, 1, 132, 87516, 140229804, 396499770810, 1671643033734960;

MATHEMATICA

t[n_, k_] := (n*k)!/Product[Product[i + j - 1, {j, 1, k}], {i, 1, n}]; Table[t[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* Amiram Eldar, Nov 17 2018 *)

CROSSREFS

T(n,n); A039622.

Cf. A000108, A005789, A005790, A005791, A060854.

Sequence in context: A327671 A036563 A025264 * A245567 A204168 A216914

Adjacent sequences:  A321713 A321714 A321715 * A321717 A321718 A321719

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Nov 17 2018

STATUS

approved

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Last modified June 4 10:51 EDT 2020. Contains 334825 sequences. (Running on oeis4.)