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A348451 Triangle read by rows: T(n,k) (1 <= k <= n) is the number of 3-extensions of an n-set over all choices of 3-partitions of the n-set.

%I A348451 #22 Oct 27 2021 11:24:58
%S A348451 1,2,1,5,4,1,14,13,6,1,41,40,25,9,1,122,121,90,48,12,1,365,364,301,
%T A348451 202,78,14,1,1094,1093,966,747,380,106,16,1,3281,3280,3025,2559,1571,
%U A348451 592,141,18,1,9842,9841,9330,8362,5864,2755,906,180,20,1
%N A348451 Triangle read by rows: T(n,k) (1 <= k <= n) is the number of 3-extensions of an n-set over all choices of 3-partitions of the n-set.
%C A348451 See Lindquist et al. 1981 for precise definition.
%H A348451 Norman Lindquist and Gerard Sierksma, <a href="https://doi.org/10.1016/0097-3165(81)90015-7">Extensions of set partitions</a>, Journal of Combinatorial Theory, Series A 31.2 (1981): 190-198. See Table III.
%e A348451 Triangle begins:
%e A348451 1,
%e A348451 2,1,
%e A348451 5,4,1,
%e A348451 14,13,6,1,
%e A348451 41,40,25,9,1,
%e A348451 122,121,90,48,12,1,
%e A348451 365,364,301,202,78,14,1,
%e A348451 1094,1093,966,747,380,106,16,1,
%e A348451 3281,3280,3025,2559,1571,592,141,18,1,
%e A348451 9842,9841,9330,8362,5864,2755,906,180,20,1,
%e A348451 ...
%Y A348451 Cf. A055248.
%Y A348451 Column 1 = A007051, column 3 = A000392.
%K A348451 nonn,tabl
%O A348451 1,2
%A A348451 _N. J. A. Sloane_, Oct 26 2021