%I
%S 2,2,5,2,15,14,2,35,84,43,2,75,350,430,142,2,155,1260,2795,2130,499,2,
%T 315,4214,15050,19880,10479,1850,2,635,13524,73143,149100,132734,
%U 51800,7193,2,1275,42350,334110,987042,1320354,854700,258948,29186,2,2555
%N Triangle read by rows: S_B(n,k) = `Type B' Stirling numbers of the second kind.
%F A partition of {n, ..., 1, 1, ..., n} into nonempty subsets X_1, ..., X_r is called `symmetric' if for each i X_i = X_j for some j. S_B(n, k) is the number of such symmetric partitions whose induced partition on {1, ..., n} involves k nonempty subsets. S_B(n, k) = S(n, k) * a(k), where S(n, k) is A008277 and a(k) is A005425.
%e S_B(2,2)=5 because the relevant partitions of {2,1,1,2} are: {2112}, {1,122}, {112,2}, {1,12,2}, {1,21,2}.
%Y Cf. A008277, A005425.
%Y S_B(n, 1)+...+S_B(n, n) = A002872(n).
%K nonn,tabl
%O 1,1
%A _James East_, Aug 15 2003
