A333900 -id:A333900 - cp's OEIS frontend

A260340 Triangle read by rows: T(n,k) = number of sets of linear n-ads in k variables.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 22, 22, 1, 1, 1, 1, 130, 550, 130, 1, 1, 1, 1, 822, 16700, 16700, 822, 1, 1, 1, 1, 6202, 703297, 3330915, 703297, 6202, 1, 1, 1, 1, 52552, 38135272, 957659906, 957659906, 38135272, 52552, 1, 1

Offset: 0

N. J. A. Sloane, Jul 30 2015

T(n,k) is the number of nonequivalent n X n binary matrices with k ones in every row and column up to permutation of rows. - Andrew Howroyd, Apr 18 2020

			Triangle begins:
  1;
  1, 1;
  1, 1,    1;
  1, 1,    1,      1;
  1, 1,    6,      1,       1;
  1, 1,   22,     22,       1,      1;
  1, 1,  130,    550,     130,      1,    1;
  1, 1,  822,  16700,   16700,    822,    1, 1;
  1, 1, 6202, 703297, 3330915, 703297, 6202, 1, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..230 (rows 0..20)
P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41.

Columns k=0..4 are A000012, A000012, A002137, A333899, A333900.
Row sums are A333891.
Cf. A008300, A133687, A257463.

T(n,k) = T(n,n-k). - Andrew Howroyd, Apr 18 2020

Extended to include k=0 and more terms added by Andrew Howroyd, Apr 18 2020

A268668 Number of factorizations of m^4 into n factors, where m is a product of exactly n distinct primes and each factor is a product of 4 primes (counted with multiplicity).

Original entry on oeis.org

1, 1, 3, 23, 465, 19834, 1532489, 193746632, 37368959742, 10437763731100, 4054349060577421, 2119978249890808761, 1452950920608600023603, 1276433147589499725385063, 1410464141866494594480406985, 1928819743142477893302566583434, 3218592064882611634798263991387049

Offset: 0

Alois P. Heinz, Feb 10 2016

nonn

Also number of ways to partition the multiset consisting of 4 copies each of 1, 2, ..., n into n multisets of size 4.

			a(2) = 3: (2*3)^4 = 1296 = 36*36 = 54*24 = 81*16.
a(3) = 23: (2*3*5)^4 = 810000 = 100*90*90 = 100*100*81 = 135*100*60 = 150*90*60 = 150*100*54 = 150*135*40 = 150*150*36 = 225*60*60 = 225*90*40 = 225*100*36 = 225*150*24 = 225*225*16 = 250*60*54 = 250*81*40 = 250*90*36 = 250*135*24 = 375*54*40 = 375*60*36 = 375*90*24 = 375*135*16 = 625*36*36 = 625*54*24 = 625*81*16.

Andrew Howroyd, Table of n, a(n) for n = 0..50

Column k=4 of A257463.

Cf. A333900.

Terms a(10) and beyond from Andrew Howroyd, Apr 18 2020

cp's OEIS Frontend

A260340 Triangle read by rows: T(n,k) = number of sets of linear n-ads in k variables.

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