OFFSET
1,3
COMMENTS
FORMULA
T(n+1, n) = n^2*(n+1)/2 = A002411(n).
T(n, n-2) = 6*T(n-1, n-3) - 15*T(n-2, n-4) + 20*T(n-3, n-5) - 15*T(n-4, n-6) + 6*T(n-5, n-7) - T(n-6, n-8), for n > 8.
T(n, n-k) = (-1)^k*Sum_{m=0..n-1} Stirling1(m+1, n-k)*binomial(n, m).
EXAMPLE
Triangle begins:
1;
1, 2;
4, 6, 3;
15, 30, 18, 4;
76, 165, 125, 40, 5;
455, 1075, 930, 380, 75, 6;
MAPLE
T := (n, k) -> local m; add(Stirling1(m+1, k)*binomial(n, m)*(-1)^(n + k), m = 0..n-1): seq(seq(T(n, k), k = 1..n), n = 1..9); # Peter Luschny, Nov 10 2023
PROG
(PARI) T(n, k) = sum(m=0, n-1, stirling(m+1, k)*binomial(n, m)*(-1)^(n+k))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Thomas Scheuerle, Nov 10 2023
STATUS
approved