|
%I #7 May 06 2016 09:35:03
%S 1,0,1,0,0,1,0,1,0,1,0,0,4,0,1,0,4,0,11,0,1,0,0,38,0,26,0,1,0,38,0,
%T 230,0,57,0,1,0,0,688,0,1148,0,120,0,1,0,688,0,7572,0,5192,0,247,0,1,
%U 0,0,20648,0,66200,0,22250,0,502,0,1
%N Triangle read by rows, T(n, k) = (n-k)*T(n-1, k-1) + k*T(n-1, k+1) except that T(n, k) = 0 if k<1 or k>n and T(n, n) = 1, for n>=0 and 0<=k<=n.
%e Triangle starts:
%e [1]
%e [0, 1]
%e [0, 0, 1]
%e [0, 1, 0, 1]
%e [0, 0, 4, 0, 1]
%e [0, 4, 0, 11, 0, 1]
%e [0, 0, 38, 0, 26, 0, 1]
%e [0, 38, 0, 230, 0, 57, 0, 1]
%e [0, 0, 688, 0, 1148, 0, 120, 0, 1]
%e [0, 688, 0, 7572, 0, 5192, 0, 247, 0, 1]
%o (Sage)
%o def T(n, k):
%o if n==k : return 1
%o if k<1 or k>n : return 0
%o return (n-k)*T(n-1,k-1)+k*T(n-1,k+1)
%o for n in range(12):
%o print([T(n, k) for k in range(n+1)])
%Y Cf. A000522 (row sums).
%K nonn,tabl
%O 0,13
%A _Peter Luschny_, May 06 2016
|
