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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

EXAMPLE

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;

  ...

PROG

(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)

CROSSREFS

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

Cf. A305027.

Sequence in context: A183610 A261365 A261507 * A090011 A061554 A296373

Adjacent sequences:  A304939 A304940 A304941 * A304943 A304944 A304945

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, May 23 2018

STATUS

approved

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Last modified February 16 09:23 EST 2019. Contains 320161 sequences. (Running on oeis4.)