cp's OEIS Frontend

A371996 Triangle read by rows: T(m, n, k) = 1 if k = 0 and T(m, n, k - 1) if k = n; otherwise (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) where m = 3.

%I A371996 #11 Apr 25 2024 09:11:41
%S A371996 1,1,1,1,9,9,1,36,297,297,1,100,2997,24273,24273,1,225,17397,493992,
%T A371996 3976209,3976209,1,441,72522,5135400,142632009,1145032281,1145032281,
%U A371996 1,784,241866,35368650,2406225609,66113123724,530050022073,530050022073
%N A371996 Triangle read by rows: T(m, n, k) = 1 if k = 0 and T(m, n, k - 1) if k = n; otherwise (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) where m = 3.
%e A371996 Triangle read by rows:
%e A371996 [0] 1;
%e A371996 [1] 1,   1;
%e A371996 [2] 1,   9,     9;
%e A371996 [3] 1,  36,   297,     297;
%e A371996 [4] 1, 100,  2997,   24273,     24273;
%e A371996 [5] 1, 225, 17397,  493992,   3976209,    3976209;
%e A371996 [6] 1, 441, 72522, 5135400, 142632009, 1145032281, 1145032281;
%p A371996 T := proc(m, n, k) option remember; if k = 0 then 1 elif k = n then T(m, n, k-1) else (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) fi end:
%p A371996 seq(seq(T(3, n, k), k = 0..n), n = 0..8));
%Y A371996 Family: A009766 (Catalan's triangle, m=0), A001498 (m=1), A060058 (m=2), this triangle (m=3), A371997 (m=4).
%Y A371996 Cf. A216966 (main diagonal).
%K A371996 nonn,tabl
%O A371996 0,5
%A A371996 _Peter Luschny_, Apr 24 2024