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%I #5 Dec 09 2018 11:41:41
%S 1,1,0,1,1,0,1,2,1,0,1,3,4,2,0,1,4,9,10,5,0,1,5,16,30,32,16,0,1,6,25,
%T 68,117,122,61,0,1,7,36,130,320,528,544,272,0,1,8,49,222,725,1684,
%U 2709,2770,1385,0,1,9,64,350,1440,4400,9856,15600,15872,7936,0,1,10,81,520,2597,9966,29125,63668,99657,101042,50521,0
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. (sec(x) + tan(x))^k.
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F E.g.f. of column k: (sec(x) + tan(x))^k.
%e E.g.f. of column k: A_k(x) = 1 + k*x/1! + k^2*x^2/2! + k*(k^2 + 1)*x^3/3! + k^2*(k^2 + 4)*x^4/4! + ...
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 0, 1, 2, 3, 4, 5, ...
%e 0, 1, 4, 9, 16, 25, ...
%e 0, 2, 10, 30, 68, 130, ...
%e 0, 5, 32, 117, 320, 725, ...
%e 0, 16, 122, 528, 1684, 4400, ...
%t Table[Function[k, n! SeriesCoefficient[(Sec[x] + Tan[x])^k, {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
%Y Columns k=0..3 give A000007, A000111, A001250, A292758.
%Y Main diagonal gives A298244.
%Y Cf. A322268.
%K nonn,tabl
%O 0,8
%A _Ilya Gutkovskiy_, Dec 01 2018
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