A352363 Triangle read by rows. The incomplete Bell transform of the swinging factorials A056040.

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 6, 11, 6, 1, 0, 6, 50, 35, 10, 1, 0, 30, 166, 225, 85, 15, 1, 0, 20, 756, 1246, 735, 175, 21, 1, 0, 140, 2932, 7588, 5761, 1960, 322, 28, 1, 0, 70, 11556, 45296, 46116, 20181, 4536, 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) = n!/floor(n/2)!^2.

Example

Triangle starts:
[0] 1;
[1] 0,   1;
[2] 0,   1,     1;
[3] 0,   2,     3,     1;
[4] 0,   6,    11,     6,     1;
[5] 0,   6,    50,    35,    10,     1;
[6] 0,  30,   166,   225,    85,    15,    1;
[7] 0,  20,   756,  1246,   735,   175,   21,   1;
[8] 0, 140,  2932,  7588,  5761,  1960,  322,  28, 1;
[9] 0,  70, 11556, 45296, 46116, 20181, 4536, 546, 36, 1;

Maple

SwingNumber := n -> n! / iquo(n, 2)!^2:
for n from 0 to 9 do
seq(IncompleteBellB(n, k, seq(SwingNumber(j), j = 0..n)), k = 0..n) od;

Crossrefs

Cf. A056040, A352364 (row sums), A352365 (alternating row sums).

Cf. A352366, A352369.

Sequence in context: A264428 A256550 A005210 * A264430 A264433 A132393

Adjacent sequences: A352360 A352361 A352362 * A352364 A352365 A352366

Keyword

nonn,tabl

Author

Peter Luschny, Mar 15 2022

Status

approved