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A158823 Triangle read by rows: matrix product A004736 * A158821. 4
1, 3, 1, 6, 2, 2, 10, 3, 4, 3, 15, 4, 6, 6, 4, 21, 5, 8, 9, 8, 5, 28, 6, 10, 12, 12, 10, 6, 36, 7, 12, 15, 16, 15, 12, 7, 45, 8, 14, 18, 20, 20, 18, 14, 8, 55, 9, 16, 21, 24, 25, 24, 21, 16, 9, 66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

FORMULA

Sum_{k=1..n} T(n, k) = A000292(n).

T(n, k) = Sum_{j=k..n} A004736(n, j)*A158821(j-1, k-1).

From R. J. Mathar, Mar 03 2011: (Start)

T(n, k) = (n-k+1)*(k-1), k>1.

T(n, 1) = A000217(n). (End)

EXAMPLE

First few rows of the triangle =

   1;

   3,  1;

   6,  2,  2;

  10,  3,  4,  3;

  15,  4,  6,  6,  4;

  21,  5,  8,  9,  8,  5;

  28,  6, 10, 12, 12, 10,  6;

  36,  7, 12, 15, 16, 15, 12,  7;

  45,  8, 14, 18, 20, 20, 18, 14,  8;

  55,  9, 16, 21, 24, 25, 24, 21, 16,  9;

  66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10;

  78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11;

  91, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12;

MAPLE

A158823 := proc(n, m) add( A004736(n, k)*A158821(k-1, m-1), k=1..n) ; end: seq(seq(A158823(n, m), m=1..n), n=1..8) ; # R. J. Mathar, Oct 22 2009

MATHEMATICA

Table[If[k==1, Binomial[n+1, 2], (n-k+1)*(k-1)], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Apr 01 2021 *)

PROG

(Magma) [k eq 1 select Binomial(n+1, 2) else (n-k+1)*(k-1): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 01 2021

(Sage) flatten([[binomial(n+1, 2) if k==1 else (n-k+1)*(k-1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Apr 01 2021

CROSSREFS

Cf. A000292 (row sums), A003991, A004736, A158821.

Sequence in context: A010467 A335320 A182182 * A184168 A122913 A289444

Adjacent sequences:  A158820 A158821 A158822 * A158824 A158825 A158826

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson & Roger L. Bagula, Mar 28 2009

EXTENSIONS

Corrected A-number in a formula - R. J. Mathar, Oct 30 2009

STATUS

approved

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Last modified April 19 20:37 EDT 2021. Contains 343117 sequences. (Running on oeis4.)