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A259919 Number of n X n upper triangular matrices (m_{i,j}) of nonnegative integers with 2 = Sum_{j=h..n} m_{h,j} - Sum_{i=1..h-1} m_{i,h} for all h in {1,...,n}. 1

%I

%S 1,1,3,22,351,11275,689146,76718466,15016410213,5018597151979,

%T 2793390337774000,2534303740130716491,3677548139455638020060,

%U 8393668597786379602398164,29683833854927200499142474520,160463839044675821511377573062150,1309702228155431081923017737636343876

%N Number of n X n upper triangular matrices (m_{i,j}) of nonnegative integers with 2 = Sum_{j=h..n} m_{h,j} - Sum_{i=1..h-1} m_{i,h} for all h in {1,...,n}.

%C a(n) counts generalized Tesler matrices. For the definition of Tesler matrices see A008608.

%e a(2) = 3: [1,1; 0,3], [2,0; 0,2], [0,2; 0,4].

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

%p `if`(i=0, b(l[1]+2, m-1, subsop(1=NULL, l)), add(

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

%p end:

%p a:= n-> b(2, n-1, [0$(n-1)]):

%p seq(a(n), n=0..10);

%Y Column k=2 of A259844.

%Y Cf. A008608.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jul 08 2015

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Last modified April 7 08:49 EDT 2020. Contains 333300 sequences. (Running on oeis4.)