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 A120666 Triangle read by rows:  T(m,n) = (n*m)!/(m!)^n. 3
 1, 1, 6, 1, 20, 1680, 1, 70, 34650, 63063000, 1, 252, 756756, 11732745024, 623360743125120, 1, 924, 17153136, 2308743493056, 1370874167589326400, 2670177736637149247308800, 1, 3432, 399072960, 472518347558400, 3177459078523411968000, 85722533226982363751829504000, 7363615666157189603982585462030336000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS T(m,n) is the number of ways to distribute n*m different toys among m different kids so that each kid gets exactly n toys. For example, with n=3 and m=2, the 6 different toys, t1, t2, t3, t4, t5 and t6, can be distributed in exactly 20 ways among the 2 kids, k1 and k2, since there are C(6,3)=20 ways to choose the three toys for k1, with the other three toys going to k2. The proof for the general case is based on the identity C(n*m,n)*C(n*m-n,n)*...*C(n*m-n*(m-1),n) = (n*m)!/(n!)^m. - Dennis P. Walsh, Apr 12 2018 LINKS Seiichi Manyama, Rows n = 1..26, flattened Eric Weisstein's World of Mathematics, Macdonald's Constant-Term Conjecture FORMULA T(m,n) = (n*m)!/(m!)^n. EXAMPLE Triangle begins: 1; 1,   6; 1,  20,   1680; 1,  70,  34650,    63063000; 1, 252, 756756, 11732745024, 623360743125120; MAPLE T:= (m, n)-> (n*m)!/(m!)^n: seq(seq(T(m, n), n=1..m), m=1..7);  # Alois P. Heinz, Apr 12 2018 MATHEMATICA v = Table[Table[(n*m)!/(m!)^n, {n, 1, m}], {m, 1, 10}]; Flatten[v] CROSSREFS Cf. A000984, A006480, A034841, A089759, A187783. Sequence in context: A146383 A264313 A096130 * A050300 A185678 A286893 Adjacent sequences:  A120663 A120664 A120665 * A120667 A120668 A120669 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Aug 11 2006 EXTENSIONS Edited by N. J. A. Sloane, Jun 17 2007 Offset corrected by Alois P. Heinz, Apr 12 2018 New name using formula by Joerg Arndt, Apr 15 2018 STATUS approved

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Last modified July 11 17:24 EDT 2020. Contains 335626 sequences. (Running on oeis4.)