OFFSET
1,5
COMMENTS
Define (n+1) X (n+1) matrices by M(n)=(binomial(i+1,j),i,j=0..n). The coefficients of the characteristic polynomials of these matrices yield the above sequence. Note : first 1 added to complete the triangle.
LINKS
Russell Merris, The p-Stirling Numbers, Turk J Math, 24 (2000), 379-399. See p. 3.
FORMULA
T(1, 1)=1, T(1, k)=0, k>1. T(n, k) = -T(n-1, k-1) + k * T(n, k-1), n>1.
abs(T(n,k)) = A008277(n,k). - Joerg Arndt, May 02 2021
EXAMPLE
Rows are
1;
1, -1;
1, -3, 1;
1, -7, 6, -1;
1, -15, 25, -10, 1;
...
25 = -(-7) + 3*6, -10 = -6 + 4*(-1).
PROG
(PARI) T(n, k) = (-1)^(k+1)*stirling(n, k, 2); \\ Michel Marcus, May 02 2021
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Feb 18 2003
STATUS
approved