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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

%I

%S 1,3,1,15,5,2,117,37,17,7,1367,418,189,100,40,23329,7027,3058,1688,

%T 939,357,570933,171428,72194,39274,24050,13429,4820,19740068,5948380,

%U 2449366,1293768,807576,517548,283510,96030

%N 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.

%C For the definition of Tesler matrices see A008608.

%C Sum_{k=1..n} k * T(n,k) = A259787(n).

%H Alois P. Heinz, <a href="/A259841/b259841.txt">Rows n = 1..20, flattened</a>

%e 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].

%e Triangle T(n,k) begins:

%e : 1;

%e : 3, 1;

%e : 15, 5, 2;

%e : 117, 37, 17, 7;

%e : 1367, 418, 189, 100, 40;

%e : 23329, 7027, 3058, 1688, 939, 357;

%e : 570933, 171428, 72194, 39274, 24050, 13429, 4820;

%p g:= u-> `if`(u=0, 0, x^u):

%p b:= proc(n, i, l) option remember; (m->`if`(m=0, [1, g(n)], `if`(i=0,

%p (p->p+[0, p[1]*g(n)])(b(l[1]+1, m-1, subsop(1=NULL, l))), add(

%p (p->p+[0, p[1]*g(j)])(b(n-j, i-1, subsop(i=l[i]+j, l)))

%p , j=0..n))))(nops(l))

%p end:

%p T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(1,n-1,[0\$(n-1)])[2]):

%p seq(T(n), n=1..10);

%Y Main diagonal gives A008608(n-1) for n>1.

%Y Column k=1 gives A259843.

%Y Row sums give A259842.

%Y Cf. A259787.

%K nonn,tabl

%O 1,2

%A _Alois P. Heinz_, Jul 06 2015

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)