A079513 - OEIS

%I #33 Jan 17 2019 17:21:14

%S 1,0,1,1,1,1,0,3,2,1,6,6,6,3,1,0,22,16,10,4,1,53,53,53,31,15,5,1,0,

%T 211,158,105,52,21,6,1,554,554,554,343,185,80,28,7,1,0,2306,1752,1198,

%U 644,301,116,36,8,1,6362,6362,6362,4056,2304,1106,462,161,45,9,1

%N Triangular array (a Riordan array) related to tennis ball problem, read by rows.

%C Riordan array (2/(2-x*c(x)+x*c(-x)), x*c(x)), with c(x) the g.f. of Catalan numbers (A000108). - _Ralf Stephan_, Dec 29 2013

%H G. C. Greubel, <a href="/A079513/b079513.txt">Rows n=0..100 of triangle, flattened</a>

%H D. Merlini, R. Sprugnoli and M. C. Verri, <a href="http://dx.doi.org/10.1006/jcta.2002.3273">The tennis ball problem</a>, J. Combin. Theory, A 99 (2002), 307-344 (Table A.2).

%e Triangle starts

%e      1;

%e      0,    1;

%e      1,    1,    1;

%e      0,    3,    2,    1;

%e      6,    6,    6,    3,    1;

%e      0,   22,   16,   10,    4,    1;

%e     53,   53,   53,   31,   15,    5,   1;

%e      0,  211,  158,  105,   52,   21,   6,   1;

%e    554,  554,  554,  343,  185,   80,  28,   7,  1;

%e      0, 2306, 1752, 1198,  644,  301, 116,  36,  8, 1;

%e   6362, 6362, 6362, 4056, 2304, 1106, 462, 161, 45, 9, 1;

%t c[t_]:= (1-Sqrt[1-4*t])/(2*t); d[t_]:= (1-(1+2*t)*Sqrt[1-4*t] -(1-2*t)*Sqrt[1+4*t] +Sqrt[1-16*t^2])/(4*t^2); g[t_, r_]:= d[t]*(t*c[t])^r; Table[SeriesCoefficient[Series[g[t, k], {t, 0, n}], n], {n, 0, 10}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Jan 16 2019 *)

%Y First column is A066357 interspersed with 0's, 2nd column gives A079514.

%Y Cf. A079514, A079515, A079516, A079517, A079518, A079519, A079520, A079521.

%K nonn,tabl

%O 0,8

%A _N. J. A. Sloane_, Jan 22 2003

%E Edited and more terms added by _Ralf Stephan_, Dec 29 2013