A188392 T(n,k) = number of (n*k) X k binary arrays with rows in nonincreasing order and n ones in every column.

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

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: A361654 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