cp's OEIS Frontend

A102323 Triangle, read by rows, where T(n,k) = T(n,k-1) + (2*k+1)*T(n-1,k) for n>k>0, T(n,0)=1 and T(n,n) = T(n,n-1) for n>=0.

%I A102323 #7 Jul 19 2024 19:05:50
%S A102323 1,1,1,1,4,4,1,13,33,33,1,40,205,436,436,1,121,1146,4198,8122,8122,1,
%T A102323 364,6094,35480,108578,197920,197920,1,1093,31563,279923,1257125,
%U A102323 3434245,6007205,6007205,1,3280,161095,2120556,13434681,51211376
%N A102323 Triangle, read by rows, where T(n,k) = T(n,k-1) + (2*k+1)*T(n-1,k) for n>k>0, T(n,0)=1 and T(n,n) = T(n,n-1) for n>=0.
%C A102323 Main diagonal is A102321, which is column 0 of triangle A102320.
%e A102323 T(5,2) = 1146 = 1*1 + 3*40 + 5*205 = 1*T(4,0) + 3*T(4,1) + 5*T(4,2).
%e A102323 T(5,2) = 1146 = 121 + 5*205 = T(5,1) + (2*2+1)*T(4,2).
%e A102323 T(5,3) = 4198 = 1146 + 7*436 = T(5,2) + (2*3+1)*T(4,3).
%e A102323 Rows begin:
%e A102323 [1],
%e A102323 [1,1],
%e A102323 [1,4,4],
%e A102323 [1,13,33,33],
%e A102323 [1,40,205,436,436],
%e A102323 [1,121,1146,4198,8122,8122],
%e A102323 [1,364,6094,35480,108578,197920,197920],
%e A102323 [1,1093,31563,279923,1257125,3434245,6007205,6007205],...
%o A102323 (PARI) T(n,k)=if(n<k||k<0,0,if(n==0||k==0,1,T(n,k-1)+(2*k+1)*T(n-1,k)))
%Y A102323 Cf. A102316, A102321, A102320.
%K A102323 nonn,tabl
%O A102323 0,5
%A A102323 _Paul D. Hanna_, Jan 05 2005