A300051 - OEIS

A300051

Triangle read by rows giving numbers T(n,j) (n >= 0, 1 <= j <= n+1) of certain restricted partitions of 2n into j blocks.

%I #10 Oct 17 2023 14:41:58

%S 1,1,1,1,5,2,1,19,24,5,1,69,202,112,14,1,251,1520,1665,510,42,1,923,

%T 11000,21121,11827,2277,132,1,3431,78806,249137,226205,76111,10010,

%U 429,1,12869,566234,2840928,3918842,2044444,456456,43472,1430

%N Triangle read by rows giving numbers T(n,j) (n >= 0, 1 <= j <= n+1) of certain restricted partitions of 2n into j blocks.

%C See Vargas (2017) for a more precise definition.

%H Jorge Garza Vargas, <a href="https://arxiv.org/abs/1709.01498">The traffic distribution of the squared unimodular random matrix and a formula for the moments of its ESD</a>, arXiv:1709.01498 [math.PR], 2017. See Table 1.

%F The authors report that they were unable to find a general formula.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 5, 2;

%e 1, 19, 24, 5;

%e 1, 69, 202, 112, 14;

%e 1, 251, 1520, 1665, 510, 42;

%e 1, 923, 11000, 21121, 11827, 2277, 132;

%e ...

%Y Main diagonal gives A000108.

%Y Columns j=1-2 give: A000012, A030662.

%K nonn,tabl

%O 0,5

%A _Michael De Vlieger_ and _N. J. A. Sloane_, Feb 23 2018