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A188392 T(n,k) = number of (n*k) X k binary arrays with rows in nonincreasing order and n ones in every column. 19
1, 2, 1, 5, 3, 1, 15, 16, 4, 1, 52, 139, 39, 5, 1, 203, 1750, 862, 81, 6, 1, 877, 29388, 35775, 4079, 150, 7, 1, 4140, 624889, 2406208, 507549, 15791, 256, 8, 1, 21147, 16255738, 238773109, 127126912, 5442547, 52450, 410, 9, 1, 115975, 504717929, 32867762616 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..181 (terms 1..69 from R. H. Hardin)

EXAMPLE

Array begins:

========================================================================

n\k| 1 2 3 4 5 6 7 8

---+--------------------------------------------------------------------

1 | 1 2 5 15 52 203 877 4140

2 | 1 3 16 139 1750 29388 624889 16255738

3 | 1 4 39 862 35775 2406208 238773109 32867762616

4 | 1 5 81 4079 507549 127126912 55643064708 38715666455777

5 | 1 6 150 15791 5442547 4762077620 8738543204786

6 | 1 7 256 52450 46757209 135029200594

7 | 1 8 410 154279 335279744

8 | 1 9 625 411180

9 | 1 10 915

...

All solutions for 6 X 2

..1..1....1..1....1..0....1..1

..1..1....1..1....1..0....1..0

..1..0....1..1....1..0....1..0

..0..1....0..0....0..1....0..1

..0..0....0..0....0..1....0..1

..0..0....0..0....0..1....0..0

PROG

(PARI)

WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}

D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); WeighT(v)[n]^k/prod(i=1, #v, i^v[i]*v[i]!)}

T(n, k)={my(m=n*k, q=Vec(exp(O(x*x^m) + intformal((x^n-1)/(1-x)))/(1-x))); if(n==0, 1, sum(j=0, m, my(s=0); forpart(p=j, s+=D(p, n, k), [1, n]); s*q[#q-j]))} \\ Andrew Howroyd, Dec 12 2018

CROSSREFS

Rows 1..8 are A000110, A020554, A165434, A165435, A165436, A165437, A188393, A188394.

Columns 3..7 are A011863(n+1), A175707, A188389, A188390, A188391.

Main diagonal gives A188388.

Cf. A188445, A219727, A330942.

Sequence in context: A188416 A160185 A283424 * A356558 A143409 A197387

Adjacent sequences: A188389 A188390 A188391 * A188393 A188394 A188395

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 30 2011

STATUS

approved

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Last modified December 1 12:40 EST 2022. Contains 358468 sequences. (Running on oeis4.)