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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 A300051 #10 Oct 17 2023 14:41:58
%S A300051 1,1,1,1,5,2,1,19,24,5,1,69,202,112,14,1,251,1520,1665,510,42,1,923,
%T A300051 11000,21121,11827,2277,132,1,3431,78806,249137,226205,76111,10010,
%U A300051 429,1,12869,566234,2840928,3918842,2044444,456456,43472,1430
%N 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.
%C A300051 See Vargas (2017) for a more precise definition.
%H A300051 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 A300051 The authors report that they were unable to find a general formula.
%e A300051 Triangle begins:
%e A300051   1;
%e A300051   1,   1;
%e A300051   1,   5,     2;
%e A300051   1,  19,    24,     5;
%e A300051   1,  69,   202,   112,    14;
%e A300051   1, 251,  1520,  1665,   510,   42;
%e A300051   1, 923, 11000, 21121, 11827, 2277, 132;
%e A300051   ...
%Y A300051 Main diagonal gives A000108.
%Y A300051 Columns j=1-2 give: A000012, A030662.
%K A300051 nonn,tabl
%O A300051 0,5
%A A300051 _Michael De Vlieger_ and _N. J. A. Sloane_, Feb 23 2018