A360660 - OEIS

%I #33 May 29 2023 08:29:56

%S 1,1,4,20,133,1027,9259,94033,1062814,13176444,177427145,2573224238,

%T 39924120823,658921572675,11513293227271,212109149134617,

%U 4105637511110979,83238756058333277,1762856698153603049,38905470655863251479,892840913430059075405

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

%C 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}.

%H Alois P. Heinz, <a href="/A360660/b360660.txt">Table of n, a(n) for n = 0..200</a>

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

%e 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].

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

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

%p     end:

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

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

%t 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}]]]];

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

%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 28 2023, after _Alois P. Heinz_ *)

%Y Main diagonal of A220886.

%Y Cf. A091058, A091059, A154323, A246107, A256070, A360664.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 15 2023