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, 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

Links

Table of n, a(n) for n=0..54.

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

Adjacent sequences: A269952 A269953 A269954 * A269956 A269957 A269958

Keyword

nonn,tabl

Author

Peter Luschny, Mar 12 2016

Status

approved