cp's OEIS Frontend

A091884 Triangle of numbers defined by Knuth.

%I A091884 #21 Dec 05 2021 06:30:17
%S A091884 1,1,1,4,3,3,27,19,20,20,256,175,191,190,190,3125,2101,2344,2312,2313,
%T A091884 2313,46656,31031,35127,34398,34462,34461,34461,823543,543607,621732,
%U A091884 605348,607535,607407,607408,607408,16777216,11012415,12692031,12301406,12366942,12360381,12360637,12360636,12360636
%N A091884 Triangle of numbers defined by Knuth.
%D A091884 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, Sect 6.4 Answer to Exer. 46.
%D A091884 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 101.
%H A091884 Seiichi Manyama, <a href="/A091884/b091884.txt">Rows n = 0..139, flattened</a>
%F A091884 T(n,k) = Sum_{j=0..k} (-1)^j * (n-j)^n.
%e A091884 Triangle begins:
%e A091884      1;
%e A091884      1,    1;
%e A091884      4,    3,    3;
%e A091884     27,   19,   20,   20;
%e A091884    256,  175,  191,  190,  190;
%e A091884   3125, 2101, 2344, 2312, 2313, 2313;
%e A091884   ...
%o A091884 (PARI) T(n,k)=if(k<0 || k>n,0,sum(j=0,k,(-1)^j*(n-j)^n))
%Y A091884 Column k=0..1 give A000312, A045531.
%Y A091884 Main diagonal gives A120485.
%K A091884 nonn,tabl
%O A091884 0,4
%A A091884 _Michael Somos_, Feb 08 2004