OFFSET
0,5
FORMULA
Given a sequence s let s|n denote the initial segment s(0), s(1), ..., s(n).
(T(s))(n, k) = IncompleteBellPolynomial(n, k, s|n) where s(n) = binomial(2*n, n).
EXAMPLE
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 2, 1;
[3] 0, 6, 6, 1;
[4] 0, 20, 36, 12, 1;
[5] 0, 70, 220, 120, 20, 1;
[6] 0, 252, 1380, 1140, 300, 30, 1;
[7] 0, 924, 8904, 10710, 4060, 630, 42, 1;
[8] 0, 3432, 59024, 101136, 52640, 11480, 1176, 56, 1;
[9] 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1;
MAPLE
CentralBinomial := n -> binomial(2*n, n):
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(CentralBinomial(j), j = 0..n)), k = 0..n) od;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 15 2022
STATUS
approved