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A269955
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.
1
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, 1, 0, 1, 126, 1563, 5788, 8165, 3906, 1, 0, 1, 254, 5067, 29404, 69765, 72426, 27391, 1, 0, 1, 510, 15963, 137884, 495845, 853146, 698719, 219192, 1
OFFSET
0,9
EXAMPLE
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, 1,
0, 1, 126, 1563, 5788, 8165, 3906, 1,
0, 1, 254, 5067, 29404, 69765, 72426, 27391, 1.
PROG
(Sage)
@cached_function
def T(k, n):
if k==n: return 1
if k==0: return 0
return sum(k^i*T(k-1, n-i) for i in (1..n-k+1))
A269955 = lambda n, k: T(k, n)
for n in (0..10): print([A269955(n, k) for k in (0..n)])
CROSSREFS
Sequence in context: A318458 A267479 A285824 * A376731 A198754 A243317
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 12 2016
STATUS
approved