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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-Fran├žois Alcover, Dec 19 2019 *)

CROSSREFS

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

Sequence in context: A163890 A298983 A128623 * A277011 A277021 A275037

Adjacent sequences:  A182698 A182699 A182700 * A182702 A182703 A182704

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Nov 27 2010

STATUS

approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)