OFFSET
0,8
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
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 15 2022
STATUS
approved