A361863 Number of set partitions of {1..n} such that the median of medians of the blocks is (n+1)/2.
1, 2, 3, 9, 26, 69, 335, 1018, 6629, 22805, 182988, 703745
Offset: 1
Examples
The a(1) = 1 through a(4) = 9 set partitions: {{1}} {{12}} {{123}} {{1234}} {{1}{2}} {{13}{2}} {{12}{34}} {{1}{2}{3}} {{124}{3}} {{13}{24}} {{134}{2}} {{14}{23}} {{1}{23}{4}} {{14}{2}{3}} {{1}{2}{3}{4}} The set partition {{1,4},{2,3}} has medians {5/2,5/2}, with median 5/2, so is counted under a(4). The set partition {{1,3},{2,4}} has medians {2,3}, with median 5/2, so is counted under a(4).
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