cp's OEIS Frontend

A371997 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 = 4.

%I A371997 #7 Apr 24 2024 12:46:02
%S A371997 1,1,1,1,17,17,1,98,1585,1585,1,354,30259,485729,485729,1,979,280883,
%T A371997 23237252,372281761,372281761,1,2275,1702758,459143300,37562889061,
%U A371997 601378506737,601378506737,1,4676,7762854,5310927050,1397160213861,113771355829478,1820943071778385,1820943071778385
%N A371997 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 = 4.
%e A371997 Triangle begins:
%e A371997 [0] 1;
%e A371997 [1] 1,    1;
%e A371997 [2] 1,   17,      17;
%e A371997 [3] 1,   98,    1585,      1585;
%e A371997 [4] 1,  354,   30259,    485729,      485729;
%e A371997 [5] 1,  979,  280883,  23237252,   372281761,    372281761;
%e A371997 [6] 1, 2275, 1702758, 459143300, 37562889061, 601378506737, 601378506737;
%p A371997 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 A371997 seq(seq(T(4, n, k), k = 0..n), n = 0..8));
%Y A371997 Family: A009766 (Catalan's triangle, m=0), A001498 (m=1), A060058 (m=2), A371996 (m=3), this triangle (m=4).
%Y A371997 Cf. A227887 (main diagonal).
%K A371997 nonn,tabl
%O A371997 0,5
%A A371997 _Peter Luschny_, Apr 24 2024