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A table distributing the values 1 2 5 14 43 144 523 2048 38486 182905 ... A047970 based on row sums of subtables counting permutations of partitions.
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%I #6 Sep 12 2024 14:45:24

%S 1,1,1,1,3,1,1,7,4,2,1,15,12,10,5,1,31,32,36,30,14,1,63,80,112,124,

%T 100,43,1,127,192,320,432,472,360,144,1,255,448,864,1360,1832,1924,

%U 1390,523,1,511,1024,2240,3958,6320,8280

%N A table distributing the values 1 2 5 14 43 144 523 2048 38486 182905 ... A047970 based on row sums of subtables counting permutations of partitions.

%C The next diagonal, 2 10 36 112 320 864 2240 ... is 1 4 12 32 80 192 448 ... plus 1 6 24 80 240 672 1792 ...

%e The table begins

%e 1

%e 1 1

%e 1 3 1

%e 1 7 4 2

%e 1 15 12 10 5

%e 1 31 32 36 30 14

%e the third diagonal is 1 4 12 32 80 192 448 ... A001787 which, in turn,

%e is the row sum of the below table

%e 1

%e 2 2

%e 3 6 3

%e 4 12 12 4

%e 5 20 30 20 5

%e which counts the permutations of

%e 3; 32, 31; 322, 321, 311; 3222, 3221, 3211, 3111; etc.

%Y Cf. A047969, A047970.

%K easy,nonn,tabl,uned

%O 1,5

%A _Alford Arnold_, Nov 03 2005