The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A188392 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#20 by Peter Luschny at Mon May 18 03:00:59 EDT 2020

STATUS

reviewed

approved

#19 by Michel Marcus at Mon May 18 00:25:11 EDT 2020

STATUS

proposed

reviewed

#18 by Andrew Howroyd at Sun May 17 15:33:34 EDT 2020

STATUS

editing

proposed

#17 by Andrew Howroyd at Sun May 17 15:31:49 EDT 2020

CROSSREFS

Rows 1..6 8 are A000110, A020554, A165434, A165435, A165436, A165437, A188393, A188394.

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

Column 4 is A175707.

Cf. A188445, A219727, A330942.

STATUS

approved

editing

#16 by Alois P. Heinz at Wed Dec 12 07:11:51 EST 2018

STATUS

editing

approved

#15 by Alois P. Heinz at Wed Dec 12 07:11:49 EST 2018

CROSSREFS

Main diagonal gives A188388.

STATUS

approved

editing

#14 by OEIS Server at Wed Dec 12 07:10:38 EST 2018

LINKS

Andrew Howroyd, <a href="/A188392/b188392_1.txt">Table of n, a(n) for n = 1..181</a> (terms 1..69 from R. H. Hardin)

#13 by Alois P. Heinz at Wed Dec 12 07:10:38 EST 2018

STATUS

proposed

approved

Discussion

Wed Dec 12

07:10

OEIS Server: Installed new b-file as b188392.txt.  Old b-file is now b188392_1.txt.

#12 by Andrew Howroyd at Wed Dec 12 00:45:11 EST 2018

STATUS

editing

proposed

#11 by Andrew Howroyd at Wed Dec 12 00:43:59 EST 2018

LINKS

R. H. Hardin, Andrew Howroyd, <a href="/A188392/b188392_1.txt">Table of n, a(n) for n = 1..181</a> (terms 1..69</a> from R. H. Hardin)

PROG

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

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=n*k, j, s+=permcount(p)*polcoef(prodD(i=1, #p, 1 + x^p[i] + O(x*x^, n), k), [1, n)^k]); s/(n*kq[#q-j]))!} \\ Andrew Howroyd, Dec 10 12 2018