login
Triangle read by rows: A113547 without its main diagonal.
1

%I #13 Dec 03 2023 18:40:20

%S 1,1,2,1,4,5,1,8,13,15,1,16,35,47,52,1,32,97,153,188,203,1,64,275,515,

%T 706,825,877,1,128,793,1785,2744,3479,3937,4140,1,256,2315,6347,11002,

%U 15177,18313,20270,21147,1,512,6817,23073,45368,68303,88033,102678,111835,115975,1,1024,20195,85475,191866,316305,436297,536882,610989,657423,678570

%N Triangle read by rows: A113547 without its main diagonal.

%C A variant of A113547 and A362924. See those entries for further information.

%e Triangle begins:

%e [1],

%e [1, 2],

%e [1, 4, 5],

%e [1, 8, 13, 15],

%e [1, 16, 35, 47, 52],

%e [1, 32, 97, 153, 188, 203],

%e [1, 64, 275, 515, 706, 825, 877],

%e [1, 128, 793, 1785, 2744, 3479, 3937, 4140],

%e [1, 256, 2315, 6347, 11002, 15177, 18313, 20270, 21147],

%e ...

%t A362926[n_,m_]:=Sum[StirlingS2[m-1,k-1]k^(n-m+1),{k,m}];

%t Table[A362926[n,m],{n,15},{m,n}] (* _Paolo Xausa_, Dec 02 2023 *)

%Y Cf. A113547, A362924.

%K nonn,tabl

%O 1,3

%A _N. J. A. Sloane_, Aug 11 2023, based on an email from _Don Knuth_.

%E Name corrected by _Paolo Xausa_, Dec 02 2023