OFFSET
0,6
COMMENTS
A tiered poset is a partially ordered set in which every maximal chain has the same length.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50).
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 2;
0, 1, 6, 6;
0, 1, 50, 36, 24;
0, 1, 510, 510, 240, 120;
0, 1, 7682, 10620, 4800, 1800, 720;
0, 1, 161406, 312606, 136920, 47040, 15120, 5040;
...
PROG
(PARI)
S(M)={my(N=matrix(#M-1, #M-1, i, j, sum(k=1, i-j+1, (2^j-1)^k*M[i-j+1, k])/j!)); for(i=1, #N, for(j=1, i, N[i, j] -= sum(k=1, j-1, N[i-k, j-k]/k!))); N}
C(n)={my(M=matrix(n+1, n+1), R=M); M[1, 1]=R[1, 1]=1; for(h=1, n, M=S(M); for(i=h, n, R[i+1, h+1] = i!*vecsum(M[i-h+1, ]))); R}
{ my(A=C(7)); for(i=1, #A, print(A[i, 1..i])) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 02 2023
STATUS
approved