|
%I #9 Mar 15 2022 08:17:02
%S 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,
%T 20,756,1246,735,175,21,1,0,140,2932,7588,5761,1960,322,28,1,0,70,
%U 11556,45296,46116,20181,4536,546,36,1
%N Triangle read by rows. The incomplete Bell transform of the swinging factorials A056040.
%F Given a sequence s let s|n denote the initial segment s(0), s(1), ..., s(n).
%F (T(s))(n, k) = IncompleteBellPolynomial(n, k, s|n), where s(n) = n!/floor(n/2)!^2.
%e Triangle starts:
%e [0] 1;
%e [1] 0, 1;
%e [2] 0, 1, 1;
%e [3] 0, 2, 3, 1;
%e [4] 0, 6, 11, 6, 1;
%e [5] 0, 6, 50, 35, 10, 1;
%e [6] 0, 30, 166, 225, 85, 15, 1;
%e [7] 0, 20, 756, 1246, 735, 175, 21, 1;
%e [8] 0, 140, 2932, 7588, 5761, 1960, 322, 28, 1;
%e [9] 0, 70, 11556, 45296, 46116, 20181, 4536, 546, 36, 1;
%p SwingNumber := n -> n! / iquo(n, 2)!^2:
%p for n from 0 to 9 do
%p seq(IncompleteBellB(n, k, seq(SwingNumber(j), j = 0..n)), k = 0..n) od;
%Y Cf. A056040, A352364 (row sums), A352365 (alternating row sums).
%Y Cf. A352366, A352369.
%K nonn,tabl
%O 0,8
%A _Peter Luschny_, Mar 15 2022
|
