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A245095 Triangle read by rows: T(n,k) = A006218(k)*A002865(n-k).

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