A352366 Triangle read by rows. The incomplete Bell transform of the Catalan numbers.

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 11, 6, 1, 0, 14, 45, 35, 10, 1, 0, 42, 199, 210, 85, 15, 1, 0, 132, 938, 1309, 700, 175, 21, 1, 0, 429, 4675, 8498, 5789, 1890, 322, 28, 1, 0, 1430, 24489, 57455, 48762, 19929, 4410, 546, 36, 1

Offset

0,8

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) = CatalanNumber(n).

Example

Triangle start:
[0] 1;
[1] 0,    1;
[2] 0,    1,     1;
[3] 0,    2,     3,     1;
[4] 0,    5,    11,     6,     1;
[5] 0,   14,    45,    35,    10,     1;
[6] 0,   42,   199,   210,    85,    15,    1;
[7] 0,  132,   938,  1309,   700,   175,   21,   1;
[8] 0,  429,  4675,  8498,  5789,  1890,  322,  28,  1;
[9] 0, 1430, 24489, 57455, 48762, 19929, 4410, 546, 36, 1;

Maple

CatalanNumber := n -> binomial(2*n, n)/(n + 1):
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(CatalanNumber(j), j=0 .. n)), k = 0..n) od;

Crossrefs

Cf. A000108, A352367 (row sums), A352368 (alternating row sums).

Cf. A352363, A352369.

Sequence in context: A173050 A172380 A144633 * A264428 A256550 A005210

Adjacent sequences: A352363 A352364 A352365 * A352367 A352368 A352369

Keyword

nonn,tabl

Author

Peter Luschny, Mar 15 2022

Status

approved