A360660 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A360660

Number of inequivalent n X n {0,1} matrices modulo permutation of the rows, with exactly n 1's.

1, 1, 4, 20, 133, 1027, 9259, 94033, 1062814, 13176444, 177427145, 2573224238, 39924120823, 658921572675, 11513293227271, 212109149134617, 4105637511110979, 83238756058333277, 1762856698153603049, 38905470655863251479, 892840913430059075405

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Also the number of multisets of n words of length n over binary alphabet where the first letter occurs n times. a(2) = 4: {aa,bb}, {ab,ab}, {ab,ba}, {ba,ba}.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) = A220886(n,n).

EXAMPLE

a(3) = 20: [111/000/000], [110/100/000], [110/010/000], [110/001/000], [101/100/000], [101/010/000], [101/001/000], [100/100/100], [100/100/010], [100/100/001], [100/011/000], [100/010/010], [100/010/001], [100/001/001], [011/010/000], [011/001/000], [010/010/010], [010/010/001], [010/001/001], [001/001/001].

MAPLE

g:= proc(n, i, j) option remember; expand(`if`(j=0, 1, `if`(i<0, 0, add(

g(n, i-1, j-k)*x^(i*k)*binomial(binomial(n, i)+k-1, k), k=0..j))))

end:

a:= n-> coeff(g(n$3), x, n):

seq(a(n), n=0..20);

MATHEMATICA

g[n_, i_, j_] := g[n, i, j] = Expand[If[j == 0, 1, If[i < 0, 0, Sum[g[n, i - 1, j - k]*x^(i*k)*Binomial[Binomial[n, i] + k - 1, k], {k, 0, j}]]]];

a[n_] := SeriesCoefficient[g[n, n, n], {x, 0, n}];

Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 28 2023, after Alois P. Heinz *)

CROSSREFS

Main diagonal of A220886.