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

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, 30, 1, 0, 685, 4816, 7231, 3360, 595, 42, 1, 0, 3192, 29952, 58632, 37856, 9800, 1120, 56, 1, 0, 19921, 199680, 493100, 416640, 147126, 24192, 1932, 72, 1

Offset: 0

Author

Peter Luschny, Jan 15 2018

Keywords

• nonn
• tabl

Examples

			Triangle starts:
0: 1;
1: 0,    1;
2: 0,    2,     1;
3: 0,    5,     6,     1;
4: 0,   12,    32,    12,     1;
5: 0,   41,   160,   110,    20,    1;
6: 0,  142,   856,   900,   280,   30,    1;
7: 0,  685,  4816,  7231,  3360,  595,   42,  1;
8: 0, 3192, 29952, 58632, 37856, 9800, 1120, 56, 1;
		

Crossrefs

T(n,1) = A009739(n), T(n,n) = A002378(n-1).

Row sums are A009248.

Cf. A075497.

Programs

Maple

gf := exp(x*exp(z)*tan(z)):
X := n -> series(gf, z, n+2):
Z := n -> n!*expand(simplify(coeff(X(n), z, n))):
A298213_row := n -> op(PolynomialTools:-CoefficientList(Z(n), x)):
seq(A298213_row(n), n=0..8);