A172603 - OEIS

%I #35 Apr 29 2023 07:01:52

%S 1,1,3432,399072960,472518347558400,3177459078523411968000,

%T 85722533226982363751829504000,7363615666157189603982585462030336000,

%U 1707750599894443404262670865631874246246400000

%N a(n) = (7n)!/(7!^n).

%C From _Tilman Piesk_, Oct 30 2014: (Start)

%C Column 7 of A187783.

%C Number of permutations of a multiset that contains n different elements 7 times.

%C Or in other words (the former title of this sequence):

%C Number of 7*n X n 0..1 arrays with row sums 1 and column sums 7.

%C (End)

%H Tilman Piesk, <a href="/A172603/b172603.txt">Table of n, a(n) for n = 0..54</a> (first 14 terms from R. H. Hardin)

%F a(n) = (7n)!/(7!^n).

%e a(3) = (7*3)!/(7!^3) = 399072960 is the number of permutations of a multiset that contains 3 different elements 7 times, e.g., {1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3}.

%p A172603:=n->(7*n)!/(5040^n): seq(A172603(n), n=0..10); # _Wesley Ivan Hurt_, Nov 01 2014

%t Table[(7 n)! / (5040^n), {n, 0, 10}] (* _Vincenzo Librandi_, Nov 01 2014 *)

%o (Magma) [Factorial(7*n)/(5040^n):  n in [0..20]]; // _Vincenzo Librandi_, Nov 01 2014

%K nonn,easy

%O 0,3

%A _R. H. Hardin_, Feb 06 2010

%E Name changed by _Tilman Piesk_, Oct 30 2014