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
Offset: 0
Keywords
Examples
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].
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..200
Crossrefs
Programs
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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 *) Table[SeriesCoefficient[Product[1/(1 - x^k)^Binomial[n, k], {k, 1, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 15 2025 *)
Formula
a(n) = A220886(n,n).
a(n) = [x^n] Product_{k=1..n} 1/(1 - x^k)^binomial(n,k). - Vaclav Kotesovec, Apr 15 2025
Comments