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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
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, 120, 88, 56, 40, 24, 16, 8, 8, 198, 135, 99, 63, 45, 27, 18, 9, 9, 300, 220, 150, 110, 70, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
By definition, the entries in row n are divisible by n.
Row sums are 1, 4, 12, 28, 60, 114, ... = n*A000070(n).
Column 1 is A228816. - Omar E. Pol, Sep 25 2013
LINKS
Robert Price, Table of n, a(n) for n = 1..5050 (First 100 rows)
FORMULA
T(n,k) = A182700(n,k), 1 <= k < n.
T(n,k) = n*A027293(n,k). - Omar E. Pol, Sep 25 2013
EXAMPLE
Triangle begins:
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;
120, 88, 56, 40, 24, 16, 8, 8;
198, 135, 99, 63, 45, 27, 18, 9, 9;
300, 220, 150, 110, 70, 50, 30, 20, 10, 10;
MAPLE
A182701 := proc(n, k) n*combinat[numbpart](n-k) ; end proc:
seq(seq(A182701(n, k), k=1..n), n=1..13) ; # R. J. Mathar, Nov 28 2010
MATHEMATICA
T[n_, k_] := n PartitionsP[n - k];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 19 2019 *)
CROSSREFS
Sequence in context: A163890 A298983 A128623 * A277011 A277021 A275037
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Nov 27 2010
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)