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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. 8

%I #26 Jun 23 2020 19:10:54

%S 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 120,88,56,40,24,16,8,8,198,135,99,63,45,27,18,9,9,300,220,150,110,70,

%U 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 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 By definition, the entries in row n are divisible by n.

%C Row sums are 1, 4, 12, 28, 60, 114, ... = n*A000070(n).

%C Column 1 is A228816. - _Omar E. Pol_, Sep 25 2013

%H Robert Price, <a href="/A182701/b182701.txt">Table of n, a(n) for n = 1..5050</a> (First 100 rows)

%F T(n,k) = A182700(n,k), 1 <= k < n.

%F T(n,k) = n*A027293(n,k). - _Omar E. Pol_, Sep 25 2013

%e Triangle begins:

%e 1;

%e 2, 2;

%e 6, 3, 3;

%e 12, 8, 4, 4;

%e 25, 15, 10, 5, 5;

%e 42, 30, 18, 12, 6, 6;

%e 77, 49, 35, 21, 14, 7, 7;

%e 120, 88, 56, 40, 24, 16, 8, 8;

%e 198, 135, 99, 63, 45, 27, 18, 9, 9;

%e 300, 220, 150, 110, 70, 50, 30, 20, 10, 10;

%p A182701 := proc(n,k) n*combinat[numbpart](n-k) ; end proc:

%p seq(seq(A182701(n,k),k=1..n),n=1..13) ; # _R. J. Mathar_, Nov 28 2010

%t T[n_, k_] := n PartitionsP[n - k];

%t Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Dec 19 2019 *)

%Y Cf. A000041, A027293, A066186, A135010, A138121, A182700, A182702.

%K nonn,tabl

%O 1,2

%A _Omar E. Pol_, Nov 27 2010

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Last modified March 28 13:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)