|
%I #10 Jun 20 2013 16:29:55
%S 1,25,1,81,20,1,25,54,15,1,100,15,36,15,1,256,60,10,27,10,1,25,128,30,
%T 5,27,10,1,100,10,64,30,5,18,10,1,81,40,5,32,10,5,9,5,1,25,27,10,0,32,
%U 10,0,9,5,1,1,5,9,10,5,16,10,5,9,5,1
%N Triangle read by rows distributing the 1602 multinomials described by A005651(6) related to Young tableau and Kostka numbers.
%C The last row (and the square roots of the first column) is 1 5 9 5 10 16 5 10 9 5 1, which when sorted appears as 1 1 5 5 5 5 9 9 10 10 16 in A003870 and A060240. The 1602 cases are distributed in A036038: 1 6 15 20 30 60 90 120 180 360 720.
%D D. Stanton and D. White, Constructive Combinatorics, 1986, page 83.
%e The triangle is:
%e 1;
%e 25, 1;
%e 81, 20, 1;
%e 25, 54, 15, 1;
%e 100, 15, 36, 15, 1;
%e 256, 60, 10, 27, 10, 1;
%e 25, 128, 30, 5, 27, 10, 1;
%e 100, 10, 64, 30, 5, 18, 10, 1;
%e 81, 40, 5, 32, 10, 5, 9, 5, 1;
%e 25, 27, 10, 0, 32, 10, 0, 9, 5, 1;
%e 1, 5, 9, 10, 5, 16, 10, 5, 9, 5, 1;
%Y Cf. A000041, A000085, A000142, A003870, A060240, A005651, A036038 and A097522 (a similar triangle distributing the 246 multinomials in A005651(5)).
%Y Cf. A104778.
%K fini,full,nonn,tabl
%O 1,2
%A _Alford Arnold_, Mar 19 2005
|
