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%I #11 Jun 13 2017 21:47:03
%S 1,1,2,3,1,4,10,16,22,1,6,21,52,105,158,211,1,8,36,116,301,644,1198,
%T 1752,2306,1,10,55,216,678,1784,4088,8144,14506,20868,27230,1,12,78,
%U 360,1320,4064,10896,25872,55354,105704,183284,260864,338444,1,14,105
%N Triangle arising from (4,2) tennis ball problem, read by rows.
%C Length of row n = 2n+1. Rows have been reversed.
%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.1).
%e Triangle starts:
%e 1;
%e 1, 2, 3;
%e 1, 4, 10, 16, 22;
%e 1, 6, 21, 52, 105, 158, 211;
%e ...
%o (PARI) T(n,k)=if(k<0 || k>2*n,0,if(n<1,k==0,sum(j=0,k,(j+1)*T(n-1,k-j))))
%Y Final diagonal gives A079489. Row sums give A066357(n+1).
%K tabf,nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 20 2003