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A188445
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T(n,k) is the number of (n*k) X k binary arrays with nonzero rows in decreasing order and n ones in every column.
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16
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1, 2, 0, 5, 1, 0, 15, 8, 0, 0, 52, 80, 5, 0, 0, 203, 1088, 205, 1, 0, 0, 877, 19232, 11301, 278, 0, 0, 0, 4140, 424400, 904580, 67198, 205, 0, 0, 0, 21147, 11361786, 101173251, 24537905, 250735, 80, 0, 0, 0, 115975, 361058000, 15207243828, 13744869502
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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Array begins:
============================================================================
n\k| 1 2 3 4 5 6 7 8 9
---+------------------------------------------------------------------------
1 | 1 2 5 15 52 203 877 4140 21147
2 | 0 1 8 80 1088 19232 424400 11361786 361058000
3 | 0 0 5 205 11301 904580 101173251 15207243828 2975725761202
4 | 0 0 1 278 67198 24537905 13744869502 11385203921707 ...
5 | 0 0 0 205 250735 425677958 1184910460297 ...
6 | 0 0 0 80 621348 5064948309 ...
7 | 0 0 0 15 1058139 ...
8 | 0 0 0 1 ...
...
Some solutions for 16 X 4:
1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0
1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1
1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1
0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0
0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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+1, q=Vec(exp(intformal(O(x^m) - x^n/(1-x)))/(1+x))); if(n==0, 1, (-1)^m*sum(j=0, m, my(s=0); forpart(p=j, s+=(-1)^#p*D(p, n, k), [1, n]); s*q[#q-j])/2)} \\ Andrew Howroyd, Dec 16 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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