A141723 - OEIS

%I #6 Mar 29 2021 01:06:30

%S 1,3,4,11,28,24,42,156,225,160,163,792,1596,1736,1120,638,3820,9855,

%T 14400,13230,8064,2510,17832,55968,102520,122265,100584,59136,9908,

%U 81368,300482,661024,968968,1005004,765765,439296,39203,365104,1549320,3975440,6910540,8653008,8112104,5845840,3294720

%N Triangle T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!), read by rows.

%H G. C. Greubel, <a href="/A141723/b141723.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!).

%e Triangle begins as:

%e      1;

%e      3,     4;

%e     11,    28,     24;

%e     42,   156,    225,    160;

%e    163,   792,   1596,   1736,   1120;

%e    638,  3820,   9855,  14400,  13230,   8064;

%e   2510, 17832,  55968, 102520, 122265,  100584,  59136;

%e   9908, 81368, 300482, 661024, 968968, 1005004, 765765, 439296;

%t Table[Sum[Multinomial[2*n-k-j, k, j], {j,0,n}], {n,0,12}, {k,0,n}]//Flatten

%o (Magma) F:= Factorial; [(&+[F(2*n)/(F(k)*F(j)*F(2*n-k-j)): j in [0..n]]): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 28 2021

%o (Sage) f=factorial; flatten([[sum(f(2*n)/(f(k)*f(j)*f(2*n-k-j)) for j in (0..n)) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 28 2021

%K nonn,tabl

%O 0,2

%A _Roger L. Bagula_, Sep 12 2008

%E Edited by _G. C. Greubel_, Mar 28 2021