A272774 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.

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, 230, 0, 57, 0, 1, 0, 0, 688, 0, 1148, 0, 120, 0, 1, 0, 688, 0, 7572, 0, 5192, 0, 247, 0, 1, 0, 0, 20648, 0, 66200, 0, 22250, 0, 502, 0, 1

Offset

0,13

Links

Table of n, a(n) for n=0..65.

Example

Triangle starts:
[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, 230, 0, 57, 0, 1]
[0, 0, 688, 0, 1148, 0, 120, 0, 1]
[0, 688, 0, 7572, 0, 5192, 0, 247, 0, 1]

Prog

(Sage)
def T(n, k):
    if n==k : return 1
    if k<1 or k>n : return 0
    return (n-k)*T(n-1, k-1)+k*T(n-1, k+1)
for n in range(12):
    print([T(n, k) for k in range(n+1)])

Crossrefs

Cf. A000522 (row sums).

Sequence in context: A111728 A359010 A143784 * A333274 A147311 A147312

Adjacent sequences: A272771 A272772 A272773 * A272775 A272776 A272777

Keyword

nonn,tabl

Author

Peter Luschny, May 06 2016

Status

approved