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A259473 Irregular triangle read by rows of coefficients arising in the enumeration of doubly stochastic matrices of integers, n >= 1, 0 <= k <= (n-1)*(n-2).

%I A259473 #21 Apr 11 2020 14:27:59
%S A259473 1,1,1,1,1,1,14,87,148,87,14,1,1,103,4306,63110,388615,1115068,
%T A259473 1575669,1115068,388615,63110,4306,103,1,1,694,184015,15902580,
%U A259473 567296265,9816969306,91422589980,490333468494,1583419977390,3166404385990,3982599815746,3166404385990
%N A259473 Irregular triangle read by rows of coefficients arising in the enumeration of doubly stochastic matrices of integers, n >= 1, 0 <= k <= (n-1)*(n-2).
%C A259473 The n-th row of A257493 is a polynomial of degree (n-1)^2. This triangle gives the coefficients of the numerator of the generating functions for A257493 with denominators being (1-x)^(1+(n-1)^2). - _Andrew Howroyd_, Apr 11 2020
%H A259473 Andrew Howroyd, <a href="/A259473/b259473.txt">Table of n, a(n) for n = 1..177</a> (rows 1..9)
%H A259473 D. M. Jackson and G. H. J. van Rees, <a href="http://www.cs.umanitoba.ca/~vanrees/enumeration.pdf">The enumeration of generalized double stochastic nonnegative integer square matrices</a>, SIAM J. Comput., 4 (1975), 474-477, doi:10.1137/0204040.
%H A259473 D. M. Jackson & G. H. J. van Rees, <a href="/A002817/a002817.pdf">The enumeration of generalized double stochastic nonnegative integer square matrices</a>, SIAM J. Comput., 4.4 (1975), 474-477. (Annotated scanned copy)
%F A259473 T(n,k) = Sum_{i=0..k} A257493(n, k-i)*(-1)^i*binomial(1+(n-1)^2,i). - _Andrew Howroyd_, Apr 11 2020
%e A259473 Triangle begins:
%e A259473   1;
%e A259473   1;
%e A259473   1,1,1;
%e A259473   1,14,87,148,87,14,1;
%e A259473   1,103,4306,63110,388615,1115068,1575669,1115068,388615,63110,4306,103,1;
%e A259473   ...
%Y A259473 Row sums are A037302.
%Y A259473 Cf. A005466, A005467, A257493.
%K A259473 nonn,tabf
%O A259473 1,7
%A A259473 _N. J. A. Sloane_, Jul 03 2015
%E A259473 a(1)=1 prepended and terms a(26) and beyond from _Andrew Howroyd_, Apr 11 2020