This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331397 #12 Mar 13 2023 06:36:18
%S A331397 1,2,14,128,1288,13472,143840,1556480,17006720,187208192,2072948224,
%T A331397 23063920640,257634273280,2887544053760,32456082448384,
%U A331397 365710391902208,4129672996618240,46721752249794560,529486122704568320,6009576477811539968,68299997524116635648
%N A331397 Number of nonnegative integer matrices with 2 distinct columns and any number of nonzero rows with column sums n and columns in decreasing lexicographic order.
%C A331397 The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.
%H A331397 Andrew Howroyd, <a href="/A331397/b331397.txt">Table of n, a(n) for n = 0..200</a>
%F A331397 a(n) = (A052141(n) + A011782(n))/2.
%F A331397 G.f.: 1/(4*sqrt(1 - 12*x + 4*x^2)) + (3 - 4*x)/(4*(1-2*x)).
%F A331397 a(n) = A011782(n) * A226994(n).
%F A331397 D-finite with recurrence n*a(n) +2*(-8*n+5)*a(n-1) +28*(2*n-3)*a(n-2) +8*(-8*n+19)*a(n-3) +16*(n-3)*a(n-4)=0. - _R. J. Mathar_, Mar 13 2023
%o A331397 (PARI) seq(n)={Vec(1/(4*sqrt(1 - 12*x + 4*x^2 + O(x*x^n))) + (3 - 4*x)/(4*(1-2*x)))} \\ _Andrew Howroyd_, Jan 15 2020
%Y A331397 Column k=2 of A331315.
%Y A331397 Cf. A011782, A052141, A226994, A331396.
%K A331397 nonn
%O A331397 0,2
%A A331397 _Andrew Howroyd_, Jan 15 2020