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 A246106 Number A(n,k) of inequivalent n X n matrices with entries from [k], where equivalence means permutations of rows or columns; square array A(n,k), n>=0, k>=0, read by antidiagonals. 26
 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 7, 1, 0, 1, 4, 27, 36, 1, 0, 1, 5, 76, 738, 317, 1, 0, 1, 6, 175, 8240, 90492, 5624, 1, 0, 1, 7, 351, 57675, 7880456, 64796982, 251610, 1, 0, 1, 8, 637, 289716, 270656150, 79846389608, 302752867740, 33642660, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..27, flattened FORMULA A(n,k) = Sum_{i=0..k} C(k,i) * A256069(n,i). EXAMPLE Square array A(n,k) begins:   1, 1,    1,        1,           1,              1, ...   0, 1,    2,        3,           4,              5, ...   0, 1,    7,       27,          76,            175, ...   0, 1,   36,      738,        8240,          57675, ...   0, 1,  317,    90492,     7880456,      270656150, ...   0, 1, 5624, 64796982, 79846389608, 20834113243925, ... MAPLE b:= proc(n, i) option remember; `if`(n=0, [[]],       `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],        b(n-i*j, i-1))[], j=1..n/i)]))     end: A:= proc(n, k) option remember; add(add(k^add(add(i[2]*j[2]*       igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)       /mul(i[1]^i[2]*i[2]!, i=t), t=b(n\$2)), s=b(n\$2))     end: seq(seq(A(n, d-n), n=0..d), d=0..10); CROSSREFS Columns k=0-10 give: A000007, A000012, A002724, A052269, A052271, A052272, A246112, A246113, A246114, A246115, A246116. Rows n=0-10 give: A000012, A001477, A039623, A058001, A058002, A058003, A058004, A246108, A246109, A246110, A246111. Main diagonal gives A246107. A028657 is a very similar array. Cf. A242095, A256069. Sequence in context: A322280 A210472 A320080 * A322836 A305466 A160114 Adjacent sequences:  A246103 A246104 A246105 * A246107 A246108 A246109 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 13 2014 STATUS approved

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Last modified May 25 01:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)