A360702 Number of sets of 2n words of length 2n over binary alphabet where each letter occurs 2n^2 times.

1, 2, 394, 10247250, 41192135957378, 26708408307353573010350, 3044454667114388718324075325130428, 65233919825974729088553743803268484284650384722, 275236371094876077407367002758415347571615535684540339803854604

Offset: 0

Author

Alois P. Heinz, Feb 16 2023

Keywords

• nonn

Comments

Also the number of inequivalent 2n X 2n {0,1} matrices with distinct rows and equal numbers of 0's and 1's, modulo permutation of the rows. a(1) = 2: [00/11], [01/10].

Examples

			a(0) = 1: {}.
a(1) = 2: {aa,bb}, {ab,ba}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A001105, A360693.

Programs

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), k=0..j))))
    end:
a:= n-> coeff(g(2*n$3), x, 2*n^2):
seq(a(n), n=0..10);

Formula

a(n) = A360693(2n,2n^2).