A269955 - OEIS

%I #8 Mar 13 2020 16:56:51

%S 1,0,1,0,1,1,0,1,6,1,0,1,14,27,1,0,1,30,123,124,1,0,1,62,459,988,645,

%T 1,0,1,126,1563,5788,8165,3906,1,0,1,254,5067,29404,69765,72426,27391,

%U 1,0,1,510,15963,137884,495845,853146,698719,219192,1

%N Triangle read by rows, T(n, k) = S(k, n) with S(n, n) = 1, S(0, n) = 0 and otherwise S(k,n) = Sum_{i=1..n-k+1} k^i*S(k-1, n-i), for n>=0 and 0<=k<=n.

%e 1,

%e 0, 1,

%e 0, 1, 1,

%e 0, 1, 6, 1,

%e 0, 1, 14, 27, 1,

%e 0, 1, 30, 123, 124, 1,

%e 0, 1, 62, 459, 988, 645, 1,

%e 0, 1, 126, 1563, 5788, 8165, 3906, 1,

%e 0, 1, 254, 5067, 29404, 69765, 72426, 27391, 1.

%o (Sage)

%o @cached_function

%o def T(k,n):

%o     if k==n: return 1

%o     if k==0: return 0

%o     return sum(k^i*T(k-1,n-i) for i in (1..n-k+1))

%o A269955 = lambda n,k: T(k,n)

%o for n in (0..10): print([A269955(n,k) for k in (0..n)])

%K nonn,tabl

%O 0,9

%A _Peter Luschny_, Mar 12 2016