cp's OEIS Frontend

A340424 Triangle read by rows: T(n,k) = A024916(n-k+1)*A002865(k-1), 1 <= k <= n.

%I A340424 #33 Jan 10 2021 11:23:12
%S A340424 1,4,0,8,0,1,15,0,4,1,21,0,8,4,2,33,0,15,8,8,2,41,0,21,15,16,8,4,56,0,
%T A340424 33,21,30,16,16,4,69,0,41,33,42,30,32,16,7,87,0,56,41,66,42,60,32,28,
%U A340424 8,99,0,69,56,82,66,84,60,56,32,12,127,0,87,69,112,82,132,84,105,64,48,14
%N A340424 Triangle read by rows: T(n,k) = A024916(n-k+1)*A002865(k-1), 1 <= k <= n.
%C A340424 Conjecture: the sum of row n equals A066186(n), the sum of all parts of all partitions of n.
%e A340424 Triangle begins:
%e A340424    1;
%e A340424    4,  0;
%e A340424    8,  0,  1;
%e A340424   15,  0,  4,  1;
%e A340424   21,  0,  8,  4,  2;
%e A340424   33,  0, 15,  8,  8,  2;
%e A340424   41,  0, 21, 15, 16   8,  4;
%e A340424   56,  0, 33, 21, 30, 16, 16,  4;
%e A340424   69,  0, 41, 33, 42, 30, 32, 16,  7;
%e A340424   87,  0, 56, 41, 66, 42, 60, 32, 28,  8;
%e A340424   99,  0, 69, 56, 82, 66, 84, 60, 56, 32, 12;
%e A340424 ...
%e A340424 For n = 6 the calculation of every term of row 6 is as follows:
%e A340424 --------------------------
%e A340424 k   A002865         T(6,k)
%e A340424 --------------------------
%e A340424 1      1   *  33   =  33
%e A340424 2      0   *  21   =   0
%e A340424 3      1   *  15   =  15
%e A340424 4      1   *   8   =   8
%e A340424 5      2   *   4   =   8
%e A340424 6      2   *   1   =   2
%e A340424 .           A024916
%e A340424 --------------------------
%e A340424 The sum of row 6 is 33 + 0 + 15 + 8 + 8 + 2 = 66, equaling A066186(6) = 66.
%Y A340424 Mirror of A245099.
%Y A340424 Columns 1, 3 and 4 are A024916 (partial sums of A000203).
%Y A340424 Column 2 gives A000004.
%Y A340424 Columns 5 and 6 give A327329.
%Y A340424 Columns 7 and 8 give A243980.
%Y A340424 Leading diagonal gives A002865.
%Y A340424 Cf. A066186.
%K A340424 nonn,tabl
%O A340424 1,2
%A A340424 _Omar E. Pol_, Jan 07 2021