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%I #5 Jan 18 2018 17:43:17
%S 1,0,1,0,2,1,0,5,6,1,0,12,32,12,1,0,41,160,110,20,1,0,142,856,900,280,
%T 30,1,0,685,4816,7231,3360,595,42,1,0,3192,29952,58632,37856,9800,
%U 1120,56,1,0,19921,199680,493100,416640,147126,24192,1932,72,1
%N Triangle read by rows, expansion of exp(x*exp(z)*tan(z)).
%e Triangle starts:
%e 0: 1;
%e 1: 0, 1;
%e 2: 0, 2, 1;
%e 3: 0, 5, 6, 1;
%e 4: 0, 12, 32, 12, 1;
%e 5: 0, 41, 160, 110, 20, 1;
%e 6: 0, 142, 856, 900, 280, 30, 1;
%e 7: 0, 685, 4816, 7231, 3360, 595, 42, 1;
%e 8: 0, 3192, 29952, 58632, 37856, 9800, 1120, 56, 1;
%p gf := exp(x*exp(z)*tan(z)):
%p X := n -> series(gf, z, n+2):
%p Z := n -> n!*expand(simplify(coeff(X(n), z, n))):
%p A298213_row := n -> op(PolynomialTools:-CoefficientList(Z(n), x)):
%p seq(A298213_row(n), n=0..8);
%Y T(n,1) = A009739(n), T(n,n) = A002378(n-1).
%Y Row sums are A009248.
%Y Cf. A075497.
%K nonn,tabl
%O 0,5
%A _Peter Luschny_, Jan 15 2018
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