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

0,5

Links

Table of n, a(n) for n=0..54.

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

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

Cf. A352363, A352366.

Sequence in context: A276891 A021830 A247686 * A111184 A111596 A271703

Adjacent sequences: A352366 A352367 A352368 * A352370 A352371 A352372

Keyword

nonn,tabl

Author

Peter Luschny, Mar 15 2022

Status

approved