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A085483 Triangle read by rows: S_B(n,k) = `Type B' Stirling numbers of the second kind. 3

%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: {-2|-1|1|2}, {-1,1|-2|2}, {-1|1|-2,2}, {-1,1|-2,2}, {1,-2|-1,2}.

%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

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Last modified December 16 01:43 EST 2019. Contains 330013 sequences. (Running on oeis4.)