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A298213 Triangle read by rows, expansion of exp(x*exp(z)*tan(z)).

%I A298213 #5 Jan 18 2018 17:43:17
%S A298213 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 A298213 30,1,0,685,4816,7231,3360,595,42,1,0,3192,29952,58632,37856,9800,
%U A298213 1120,56,1,0,19921,199680,493100,416640,147126,24192,1932,72,1
%N A298213 Triangle read by rows, expansion of exp(x*exp(z)*tan(z)).
%e A298213 Triangle starts:
%e A298213 0: 1;
%e A298213 1: 0,    1;
%e A298213 2: 0,    2,     1;
%e A298213 3: 0,    5,     6,     1;
%e A298213 4: 0,   12,    32,    12,     1;
%e A298213 5: 0,   41,   160,   110,    20,    1;
%e A298213 6: 0,  142,   856,   900,   280,   30,    1;
%e A298213 7: 0,  685,  4816,  7231,  3360,  595,   42,  1;
%e A298213 8: 0, 3192, 29952, 58632, 37856, 9800, 1120, 56, 1;
%p A298213 gf := exp(x*exp(z)*tan(z)):
%p A298213 X := n -> series(gf, z, n+2):
%p A298213 Z := n -> n!*expand(simplify(coeff(X(n), z, n))):
%p A298213 A298213_row := n -> op(PolynomialTools:-CoefficientList(Z(n), x)):
%p A298213 seq(A298213_row(n), n=0..8);
%Y A298213 T(n,1) = A009739(n), T(n,n) = A002378(n-1).
%Y A298213 Row sums are A009248.
%Y A298213 Cf. A075497.
%K A298213 nonn,tabl
%O A298213 0,5
%A A298213 _Peter Luschny_, Jan 15 2018