cp's OEIS Frontend

A259097 Triangle read by rows: T(n,r) = binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1), n >= 2, r = 0..floor(n/2)-1.

%I A259097 #19 Sep 08 2022 08:46:13
%S A259097 1,1,2,2,5,5,14,15,5,42,49,21,132,168,84,14,429,594,336,84,1430,2145,
%T A259097 1350,420,42,4862,7865,5445,1980,330,16796,29172,22022,9075,1980,132,
%U A259097 58786,109174,89232,40898,10725,1287,208012,411502,361998,182182,55055,9009,429,742900,1560090,1469650,804440,273273,55055,5005
%N A259097 Triangle read by rows: T(n,r) = binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1), n >= 2, r = 0..floor(n/2)-1.
%H A259097 Indranil Ghosh, <a href="/A259097/b259097.txt">Rows 2..125, flattened</a>
%H A259097 F. R. Bernhart & N. J. A. Sloane, <a href="/A006343/a006343.pdf">Emails, April-May 1994</a>
%e A259097 Triangle begins:
%e A259097         1;
%e A259097         1;
%e A259097         2,       2;
%e A259097         5,       5;
%e A259097        14,      15,       5;
%e A259097        42,      49,      21;
%e A259097       132,     168,      84,      14;
%e A259097       429,     594,     336,      84;
%e A259097      1430,    2145,    1350,     420,      42;
%e A259097      4862,    7865,    5445,    1980,     330;
%e A259097     16796,   29172,   22022,    9075,    1980,    132;
%e A259097     58786,  109174,   89232,   40898,   10725,   1287;
%e A259097    208012,  411502,  361998,  182182,   55055,   9009,   429;
%e A259097    742900, 1560090, 1469650,  804440,  273273,  55055,  5005;
%e A259097   2674440, 5943200, 5969040, 3527160, 1324960, 312312, 40040, 1430;
%e A259097   ...
%p A259097 T:=(n,r) -> binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1);
%p A259097 v:=n->[seq(T(n,r),r=0..floor(n/2)-1)];
%p A259097 for n from 2 to 16 do lprint(v(n)); od:
%t A259097 Flatten[Table[Binomial[n,r] Binomial[2n-3r-4,n-2r-2]/(n-r-1),{n,2,16},{r,0,Floor[(n/2)]-1}]] (* _Indranil Ghosh_, Feb 20 2017 *)
%o A259097 (Magma) /* As triangle: */ [[Binomial(n,k)*Binomial(2*n-3*k-4,n-2*k-2)/(n-k-1): k in [0..Floor(n/2)-1]]: n in [2..15]]; // _Vincenzo Librandi_, Jun 22 2015
%Y A259097 Row sums are A006343. Right-hand boundary is a mixture of A000108 and A002054.
%K A259097 nonn,tabf
%O A259097 2,3
%A A259097 _N. J. A. Sloane_, Jun 22 2015