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Triangle, generated from A111579.
2

%I #20 Jun 30 2023 05:08:18

%S 1,1,1,1,1,1,1,2,1,1,1,5,3,1,1,1,15,11,4,1,1,1,52,49,19,5,1,1,1,203,

%T 257,109,29,6,1,1,1,877,1539,742,201,41,7,1,1,1,4140,10299,5815,1657,

%U 331,55,8,1,1,1,21147,75905,51193,15821,3176,505,71,9,1,1,1,115975,609441,498118,170389,35451,5497,729,89,10,1,1

%N Triangle, generated from A111579.

%C Columns are inverse binomial transforms of columns (k>0) of A111579.

%H A. Kerber, <a href="https://doi.org/10.1016/0012-365X(78)90163-2">A matrix of combinatorial numbers related to the symmetric groups</a>, Discrete Math., 21 (1978), 319-321.

%H A. Kerber, <a href="/A004211/a004211.pdf">A matrix of combinatorial numbers related to the symmetric groups</a>, Discrete Math., 21 (1978), 319-321. [Annotated scanned copy]

%e First few rows of the triangle are:

%e 1,

%e 1, 1,

%e 1, 1, 1,

%e 1, 2, 1, 1,

%e 1, 5, 3, 1, 1,

%e 1, 15, 11, 4, 1, 1,

%e 1, 52, 49, 19, 5, 1, 1,

%e 1, 203, 257, 109, 29, 6, 1, 1,

%e 1, 877, 1539, 742, 201, 41, 7, 1, 1,

%e 1, 4140, 10299, 5815, 1657, 331, 55, 8, 1, 1,

%e ...

%e Inverse binomial transform of column 2 of A111579 (1, 2, 5, 15, 52, 203...) = column 2 (1, 1, 2, 5, 15, 52...).

%Y Cf. A111579, A008277.

%Y For two other versions of this triangle see A241578, A241579.

%Y Rows and columns give A000110, A004211, A004212, A004213, A005011, A005012, A028387, A241577.

%K nonn,tabl

%O 0,8

%A _Gary W. Adamson_, Aug 14 2005

%E More terms from _N. J. A. Sloane_, Apr 29 2014