A304942 Triangle read by rows: T(n,k) is the number of nonisomorphic binary n X n matrices with k 1's per column under row and column permutations.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 11, 5, 1, 1, 7, 35, 35, 7, 1, 1, 11, 132, 410, 132, 11, 1, 1, 15, 471, 6178, 6178, 471, 15, 1, 1, 22, 1806, 122038, 594203, 122038, 1806, 22, 1, 1, 30, 7042, 2921607, 85820809, 85820809, 2921607, 7042, 30, 1

Offset: 0

Author

Andrew Howroyd, May 23 2018

Keywords

• nonn
• tabl

Examples

			Triangle begins (n >=0, k >= 0):
  1;
  1,  1;
  1,  2,    1;
  1,  3,    3,      1;
  1,  5,   11,      5,      1;
  1,  7,   35,     35,      7,      1;
  1, 11,  132,    410,    132,     11,    1;
  1, 15,  471,   6178,   6178,    471,   15,  1;
  1, 22, 1806, 122038, 594203, 122038, 1806, 22, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..527
• StackExchange, How many arrays with crossed cells, order of rows/columns irrelevant, Dec 13 2013

Crossrefs

Columns k=1..5 are A000041, A247417, A247596, A247597, A247598.

Cf. A305027.

Programs

PARI

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
K(q,t,k)={polcoeff(prod(j=1, #q, my(g=gcd(t, q[j])); (1 + x^(q[j]/g) + O(x*x^k))^g), k)}
Blocks(n,m,k)={my(s=0); forpart(q=m, s+=permcount(q)*polcoeff(exp(sum(t=1, n, K(q,t,k)/t*x^t) + O(x*x^n)), n)); s/m!}
for(n=0, 10, for(k=0, n, print1(Blocks(n,n,k), ", ")); print)