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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 October 20 16:05 EDT 2019. Contains 328268 sequences. (Running on oeis4.)