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%I #16 Sep 04 2023 06:07:33
%S 1,0,3,1,0,5,1,3,0,8,2,3,5,0,10,2,6,5,8,0,14,4,6,10,8,10,0,16,4,12,10,
%T 16,10,14,0,20,7,12,20,16,20,14,16,0,23,8,21,20,32,20,28,16,20,0,27,
%U 12,24,35,32,40,28,32,20,23,0,29,14,36,40,56,40,56,32,40,23,27,0,35
%N Triangle read by rows: T(n,k) = A006218(k)*A002865(n-k).
%C Row sums give A006128, n >= 1.
%C Column 1 is A002865.
%C Leading diagonal is A006218, n >= 1.
%C For another version see A221530.
%H Paolo Xausa, <a href="/A245095/b245095.txt">Table of n, a(n) for n = 1..11325</a> (rows 1..150 of the triangle, flattened)
%e Triangle begins:
%e 1;
%e 0, 3;
%e 1, 0, 5;
%e 1, 3, 0, 8;
%e 2, 3, 5, 0, 10;
%e 2, 6, 5, 8, 0, 14;
%e 4, 6, 10, 8, 10, 0, 16;
%e 4, 12, 10, 16, 10, 14, 0, 20;
%e 7, 12, 20, 16, 20, 14, 16, 0, 23;
%e 8, 21, 20, 32, 20, 28, 16, 20, 0, 27;
%e 12, 24, 35, 32, 40, 28, 32, 20, 23, 0, 29;
%e 14, 36, 40, 56, 40, 56, 32, 40, 23, 27, 0, 35;
%e ...
%e For n = 6:
%e -------------------------
%e k A006218 T(6,k)
%e -------------------------
%e 1 1 * 2 = 2
%e 2 3 * 2 = 6
%e 3 5 * 1 = 5
%e 4 8 * 1 = 8
%e 5 10 * 0 = 0
%e 6 14 * 1 = 14
%e . A002865
%e -------------------------
%e So row 6 is [2, 6, 5, 8, 0, 14] and the sum of row 6 is 2+6+5+8+0+14 = 35 equaling A006128(6) = 35.
%t A245095row[n_]:=Accumulate[DivisorSigma[0,Range[n]]]Reverse[Differences[PartitionsP[Range[-1,n-1]]]];Array[A245095row,10] (* _Paolo Xausa_, Sep 04 2023 *)
%o (PARI) a006218(n) = sum(k=1, n, n\k);
%o a002865(n) = if(n, numbpart(n)-numbpart(n-1), 1);
%o row(n) = vector(n, i, a006218(i)*a002865(n-i)); \\ _Michel Marcus_, Jul 18 2014
%Y Cf. A000005, A000041, A002865, A006128, A006218, A221529, A221530, A245099.
%K nonn,tabl
%O 1,3
%A _Omar E. Pol_, Jul 14 2014
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