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A188392
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T(n,k) = number of (n*k) X k binary arrays with rows in nonincreasing order and n ones in every column.
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19
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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