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%I #10 Mar 15 2022 08:17:23
%S 1,0,1,0,2,1,0,6,6,1,0,20,36,12,1,0,70,220,120,20,1,0,252,1380,1140,
%T 300,30,1,0,924,8904,10710,4060,630,42,1,0,3432,59024,101136,52640,
%U 11480,1176,56,1,0,12870,400824,966672,671328,195300,27720,2016,72,1
%N Triangle read by rows. The incomplete Bell transform of the central binomial numbers.
%F Given a sequence s let s|n denote the initial segment s(0), s(1), ..., s(n).
%F (T(s))(n, k) = IncompleteBellPolynomial(n, k, s|n) where s(n) = binomial(2*n, n).
%e Triangle starts:
%e [0] 1;
%e [1] 0, 1;
%e [2] 0, 2, 1;
%e [3] 0, 6, 6, 1;
%e [4] 0, 20, 36, 12, 1;
%e [5] 0, 70, 220, 120, 20, 1;
%e [6] 0, 252, 1380, 1140, 300, 30, 1;
%e [7] 0, 924, 8904, 10710, 4060, 630, 42, 1;
%e [8] 0, 3432, 59024, 101136, 52640, 11480, 1176, 56, 1;
%e [9] 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1;
%p CentralBinomial := n -> binomial(2*n, n):
%p for n from 0 to 9 do
%p seq(IncompleteBellB(n, k, seq(CentralBinomial(j), j = 0..n)), k = 0..n) od;
%Y Cf. A000984, A352370 (row sums), A352371 (alternating row sums).
%Y Cf. A352363, A352366.
%K nonn,tabl
%O 0,5
%A _Peter Luschny_, Mar 15 2022
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