cp's OEIS Frontend

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

%I A360702 #22 Feb 19 2023 02:40:17
%S A360702 1,2,394,10247250,41192135957378,26708408307353573010350,
%T A360702 3044454667114388718324075325130428,
%U A360702 65233919825974729088553743803268484284650384722,275236371094876077407367002758415347571615535684540339803854604
%N A360702 Number of sets of 2n words of length 2n over binary alphabet where each letter occurs 2n^2 times.
%C A360702 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].
%H A360702 Alois P. Heinz, <a href="/A360702/b360702.txt">Table of n, a(n) for n = 0..30</a>
%F A360702 a(n) = A360693(2n,2n^2).
%e A360702 a(0) = 1: {}.
%e A360702 a(1) = 2: {aa,bb}, {ab,ba}.
%p A360702 g:= proc(n, i, j) option remember; expand(`if`(j=0, 1, `if`(i<0, 0, add(
%p A360702       g(n, i-1, j-k)*x^(i*k)*binomial(binomial(n, i), k), k=0..j))))
%p A360702     end:
%p A360702 a:= n-> coeff(g(2*n$3), x, 2*n^2):
%p A360702 seq(a(n), n=0..10);
%Y A360702 Cf. A001105, A360693.
%K A360702 nonn
%O A360702 0,2
%A A360702 _Alois P. Heinz_, Feb 16 2023