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 A259841 Number T(n,k) of elements k in all n X n Tesler matrices of nonnegative integers; triangle T(n,k), n>=1, 1<=k<=n, read by rows. 5
 1, 3, 1, 15, 5, 2, 117, 37, 17, 7, 1367, 418, 189, 100, 40, 23329, 7027, 3058, 1688, 939, 357, 570933, 171428, 72194, 39274, 24050, 13429, 4820, 19740068, 5948380, 2449366, 1293768, 807576, 517548, 283510, 96030 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For the definition of Tesler matrices see A008608. Sum_{k=1..n} k * T(n,k) = A259787(n). LINKS Alois P. Heinz, Rows n = 1..20, flattened EXAMPLE There are two 2 X 2 Tesler matrices: [1,0; 0,1], [0,1; 0,2], containing three 1's and one 2, thus row 2 gives [3, 1]. Triangle T(n,k) begins: :      1; :      3,      1; :     15,      5,     2; :    117,     37,    17,     7; :   1367,    418,   189,   100,    40; :  23329,   7027,  3058,  1688,   939,   357; : 570933, 171428, 72194, 39274, 24050, 13429, 4820; MAPLE g:= u-> `if`(u=0, 0, x^u): b:= proc(n, i, l) option remember; (m->`if`(m=0, [1, g(n)], `if`(i=0,      (p->p+[0, p[1]*g(n)])(b(l[1]+1, m-1, subsop(1=NULL, l))), add(      (p->p+[0, p[1]*g(j)])(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=1..n))(b(1, n-1, [0\$(n-1)])[2]): seq(T(n), n=1..10); CROSSREFS Main diagonal gives A008608(n-1) for n>1. Column k=1 gives A259843. Row sums give A259842. Cf. A259787. Sequence in context: A121335 A126454 A293558 * A228540 A144815 A065250 Adjacent sequences:  A259838 A259839 A259840 * A259842 A259843 A259844 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 06 2015 STATUS approved

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Last modified February 27 06:36 EST 2020. Contains 332299 sequences. (Running on oeis4.)