A352369 - OEIS

%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