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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, 91 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..79.

FORMULA

sum_{m=1..n} T(n,m) = A000292(n).

T(n,m) = sum_{k=m..n} A004736(n,k)*A158821(k-1,m-1).

T(n,1) = A000217(n). T(n,k) = (n-k+1)*(k-1), k>1. - R. J. Mathar, Mar 03 2011

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

CROSSREFS

Cf. A158821, A000292  (row sums), A003991

Sequence in context: A104573 A010467 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 July 21 20:57 EDT 2017. Contains 289648 sequences.