OFFSET
0,9
COMMENTS
Here weakly graded means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..860 (rows 0..40)
Andrew Howroyd, PARI Program, Apr 2023.
Wikipedia, Graded poset.
FORMULA
G.f. of column k >= 2: C(k,x)/C(k-1,x) - C(k-1,x)/C(k-2,x) where C(k,x) is the g.f. of column k of A361952.
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 3, 1;
0, 1, 8, 6, 1;
0, 1, 20, 30, 9, 1;
0, 1, 55, 145, 66, 12, 1;
0, 1, 163, 745, 465, 111, 15, 1;
0, 1, 556, 4245, 3444, 964, 165, 18, 1;
...
PROG
(PARI) \\ See link for program code.
{ my(A=A361953tabl(8)); for(i=1, #A, print(A[i, 1..i])) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 31 2023
STATUS
approved