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A182701 Triangle T(n,k) = n*A000041(n-k) read by rows, 1 <= k <= n. Sum of the parts of all partitions of n that contain k as a part.

%I A182701 #26 Jun 23 2020 19:10:54
%S A182701 1,2,2,6,3,3,12,8,4,4,25,15,10,5,5,42,30,18,12,6,6,77,49,35,21,14,7,7,
%T A182701 120,88,56,40,24,16,8,8,198,135,99,63,45,27,18,9,9,300,220,150,110,70,
%U A182701 50,30,20,10,10,462,330,242,165,121,77,55,33,22,11,11,672,504,360,264,180,132,84,60,36,24,12,12
%N A182701 Triangle T(n,k) = n*A000041(n-k) read by rows, 1 <= k <= n. Sum of the parts of all partitions of n that contain k as a part.
%C A182701 By definition, the entries in row n are divisible by n.
%C A182701 Row sums are 1, 4, 12, 28, 60, 114, ... = n*A000070(n).
%C A182701 Column 1 is A228816. - _Omar E. Pol_, Sep 25 2013
%H A182701 Robert Price, <a href="/A182701/b182701.txt">Table of n, a(n) for n = 1..5050</a> (First 100 rows)
%F A182701 T(n,k) = A182700(n,k), 1 <= k < n.
%F A182701 T(n,k) = n*A027293(n,k). - _Omar E. Pol_, Sep 25 2013
%e A182701 Triangle begins:
%e A182701     1;
%e A182701     2,   2;
%e A182701     6,   3,   3;
%e A182701    12,   8,   4,   4;
%e A182701    25,  15,  10,   5,   5;
%e A182701    42,  30,  18,  12,   6,   6;
%e A182701    77,  49,  35,  21,  14,   7,   7;
%e A182701   120,  88,  56,  40,  24,  16,   8,   8;
%e A182701   198, 135,  99,  63,  45,  27,  18,   9,   9;
%e A182701   300, 220, 150, 110,  70,  50,  30,  20,  10,  10;
%p A182701 A182701 := proc(n,k) n*combinat[numbpart](n-k) ; end proc:
%p A182701 seq(seq(A182701(n,k),k=1..n),n=1..13) ; # _R. J. Mathar_, Nov 28 2010
%t A182701 T[n_, k_] := n PartitionsP[n - k];
%t A182701 Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Dec 19 2019 *)
%Y A182701 Cf. A000041, A027293, A066186, A135010, A138121, A182700, A182702.
%K A182701 nonn,tabl
%O A182701 1,2
%A A182701 _Omar E. Pol_, Nov 27 2010