cp's OEIS Frontend

A112996 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.

%I A112996 #6 Sep 12 2024 14:45:24
%S A112996 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 A112996 100,43,1,127,192,320,432,472,360,144,1,255,448,864,1360,1832,1924,
%U A112996 1390,523,1,511,1024,2240,3958,6320,8280
%N A112996 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 A112996 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 A112996 The table begins
%e A112996 1
%e A112996 1 1
%e A112996 1 3 1
%e A112996 1 7 4 2
%e A112996 1 15 12 10 5
%e A112996 1 31 32 36 30 14
%e A112996 the third diagonal is 1 4 12 32 80 192 448 ... A001787 which, in turn,
%e A112996 is the row sum of the below table
%e A112996 1
%e A112996 2 2
%e A112996 3 6 3
%e A112996 4 12 12 4
%e A112996 5 20 30 20 5
%e A112996 which counts the permutations of
%e A112996 3; 32, 31; 322, 321, 311; 3222, 3221, 3211, 3111; etc.
%Y A112996 Cf. A047969, A047970.
%K A112996 easy,nonn,tabl,uned
%O A112996 1,5
%A A112996 _Alford Arnold_, Nov 03 2005