A352369 Triangle read by rows. The incomplete Bell transform of the central binomial numbers.

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, 300, 30, 1, 0, 924, 8904, 10710, 4060, 630, 42, 1, 0, 3432, 59024, 101136, 52640, 11480, 1176, 56, 1, 0, 12870, 400824, 966672, 671328, 195300, 27720, 2016, 72, 1

Offset: 0

Author

Peter Luschny, Mar 15 2022

Keywords

• nonn
• tabl

Examples

			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;
		

Crossrefs

Cf. A000984, A352370 (row sums), A352371 (alternating row sums).

Cf. A352363, A352366.

Programs

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;

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).