%I #21 Dec 05 2021 06:30:17

%S 1,1,1,4,3,3,27,19,20,20,256,175,191,190,190,3125,2101,2344,2312,2313,

%T 2313,46656,31031,35127,34398,34462,34461,34461,823543,543607,621732,

%U 605348,607535,607407,607408,607408,16777216,11012415,12692031,12301406,12366942,12360381,12360637,12360636,12360636

%N Triangle of numbers defined by Knuth.

%D D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, Sect 6.4 Answer to Exer. 46.

%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 101.

%H Seiichi Manyama, <a href="/A091884/b091884.txt">Rows n = 0..139, flattened</a>

%F T(n,k) = Sum_{j=0..k} (-1)^j * (n-j)^n.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 4, 3, 3;

%e 27, 19, 20, 20;

%e 256, 175, 191, 190, 190;

%e 3125, 2101, 2344, 2312, 2313, 2313;

%e ...

%o (PARI) T(n,k)=if(k<0 || k>n,0,sum(j=0,k,(-1)^j*(n-j)^n))

%Y Column k=0..1 give A000312, A045531.

%Y Main diagonal gives A120485.

%K nonn,tabl

%O 0,4

%A _Michael Somos_, Feb 08 2004