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Number T(n,k) of entries in the k-th blocks of all set partitions of [n] when blocks are ordered by decreasing lengths (and increasing smallest elements); triangle T(n,k), n>=1, 1<=k<=n, read by rows.

OEIS Parity Triangles@oeistriangles.peterkagey.com

OEIS sequence A319375 by Alois P. Heinz (December 2018). (Even terms are drawn as dark hexagons and odd terms are drawn as light hexagons.)

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