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A248686 Triangular array of multinomial coefficients :  T(n,k) = n!/(n(1)!*n(2)!* ...*n(k)!), where n(i) = floor((n + i - 1)/k) for i = 1 .. k. 2
1, 1, 2, 1, 3, 6, 1, 6, 12, 24, 1, 10, 30, 60, 120, 1, 20, 90, 180, 360, 720, 1, 35, 210, 630, 1260, 2520, 5040, 1, 70, 560, 2520, 5040, 10080, 20160, 40320, 1, 126, 1680, 7560, 22680, 45360, 90720, 181440, 362880, 1, 252, 4200, 25200, 113400, 226800, 453600 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..5000

EXAMPLE

First seven rows:

1

1   2

1   3    6

1   6    12   24

1   10   30   60    120

1   20   90   180   360    720

1   35   210  630   1260   2520   5040

Writing floor as [ ], the numbers comprising row 4 are

T(4,1) = 4!/[4/1]! = 24/24 = 1

T(4,2) = 4!/([4/2]![5/2]!) = 24/(2*2) = 6

T(4,3) = 4!/([4/3]![5/3]![6/3]! = 24/(1*1*2) = 12

T(4,4) = 4!/([4/4]![5/4]![6/4]![7/4]!) = 24/(1*1*1*1) = 24.

MATHEMATICA

f[n_, k_] := f[n, k] = n!/Product[Floor[(n + i)/k]!, {i, 0, k - 1}]

t = Table[f[n, k], {n, 0, 10}, {k, 1, n}];

u = Flatten[t]  (* A248686 sequence *)

TableForm[t]    (* A248686 array *)

Table[Sum[f[n, k], {k, 1, n}], {n, 1, 22}] (* A248687 *)

CROSSREFS

Cf. A248687.

Sequence in context: A059298 A214306 A156914 * A059434 A182928 A141476

Adjacent sequences:  A248683 A248684 A248685 * A248687 A248688 A248689

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 11 2014

STATUS

approved

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Last modified June 23 21:29 EDT 2017. Contains 288675 sequences.