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A188445 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. 14
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 (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)

FORMULA

A(n,k) = 0 for n > 2^(k-1). - Andrew Howroyd, Jan 24 2020

EXAMPLE

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

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+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

CROSSREFS

Rows 1..5 are A000110, A002718, A060486, A188446, A188447.

Columns 5..6 are A331127, A331129.

Column sums are A319190.

Cf. A059443, A060487, A188392, A219585, A318361, A330942, A330964, A331039.

Sequence in context: A201730 A188449 A177267 * A327806 A319683 A294137

Adjacent sequences:  A188442 A188443 A188444 * A188446 A188447 A188448

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 31 2011

STATUS

approved

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Last modified February 22 10:32 EST 2020. Contains 332134 sequences. (Running on oeis4.)