The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A079513 Triangular array (a Riordan array) related to tennis ball problem, read by rows. 11
 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, 211, 158, 105, 52, 21, 6, 1, 554, 554, 554, 343, 185, 80, 28, 7, 1, 0, 2306, 1752, 1198, 644, 301, 116, 36, 8, 1, 6362, 6362, 6362, 4056, 2304, 1106, 462, 161, 45, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS 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 LINKS G. C. Greubel, Rows n=0..100 of triangle, flattened D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344 (Table A.2). EXAMPLE Triangle starts      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,  211,  158,  105,   52,   21,   6,   1;    554,  554,  554,  343,  185,   80,  28,   7,  1;      0, 2306, 1752, 1198,  644,  301, 116,  36,  8, 1;   6362, 6362, 6362, 4056, 2304, 1106, 462, 161, 45, 9, 1; MATHEMATICA 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 *) CROSSREFS First column is A066357 interspersed with 0's, 2nd column gives A079514. Cf. A079514, A079515, A079516, A079517, A079518, A079519, A079520, A079521. Sequence in context: A208520 A114155 A192018 * A060408 A267121 A208518 Adjacent sequences:  A079510 A079511 A079512 * A079514 A079515 A079516 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jan 22 2003 EXTENSIONS Edited and more terms added by Ralf Stephan, Dec 29 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 23 12:15 EDT 2021. Contains 343204 sequences. (Running on oeis4.)