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A259786 Number T(n,k) of n X n Tesler matrices of nonnegative integers with element sum n+k; triangle T(n,k), n>=1, 0<=k<=n*(n-1)/2, read by rows. 3
1, 1, 1, 1, 3, 2, 1, 1, 6, 11, 11, 7, 3, 1, 1, 10, 35, 65, 81, 71, 50, 27, 12, 4, 1, 1, 15, 85, 260, 526, 771, 878, 811, 627, 416, 238, 118, 50, 18, 5, 1, 1, 21, 175, 805, 2436, 5362, 9123, 12568, 14465, 14289, 12345, 9483, 6534, 4071, 2297, 1176, 542, 224, 81, 25, 6, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

For the definition of Tesler matrices see A008608.

Sum_{k=0..n*(n-1)/2} (n+k) * T(n,k) = A259787(n).

LINKS

Alois P. Heinz, Rows n = 1..17, flattened

EXAMPLE

Triangle T(n,k) begins:

1;

1,  1;

1,  3,  2,   1;

1,  6, 11,  11,   7,   3,   1;

1, 10, 35,  65,  81,  71,  50,  27,  12,   4,   1;

1, 15, 85, 260, 526, 771, 878, 811, 627, 416, 238, 118, 50, 18, 5, 1;

MAPLE

b:= proc(n, i, l) option remember; (m-> `if`(m=0, 1, expand(

      `if`(i=0, x^(l[1]+1)*b(l[1]+1, m-1, subsop(1=NULL, l)), add(

       b(n-j, i-1, subsop(i=l[i]+j, l)), j=0..n)))))(nops(l))

    end:

T:= n->(p->seq(coeff(p, x, i), i=n-1..degree(p)))(b(1, n-1, [0$(n-1)])):

seq(T(n), n=1..8);

CROSSREFS

Row sums give A008608.

Cf. A000217, A259787.

Sequence in context: A058280 A113185 A132069 * A254410 A073201 A118654

Adjacent sequences:  A259783 A259784 A259785 * A259787 A259788 A259789

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Jul 05 2015

STATUS

approved

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Last modified February 19 11:04 EST 2018. Contains 299330 sequences. (Running on oeis4.)