OFFSET
0,10
LINKS
Peter Luschny, The Bell transform
EXAMPLE
Irregular table (the refinement is indicated by round brackets) starts:
[0] [1]
[1] [1, 1]
[2] [1, (1, 1), 1]
[3] [1, (1, 2, 1), (3, 1), 1]
[4] [1, (1, 3, 3, 1), (4, 3, 5, 1), (6, 1), 1]
[5] [1, (1, 4, 6, 4, 1), (5, 10, 9, 8, 7, 1), (10, 15, 9, 1), (10, 1), 1]
[6] [1, (1, 5, 10, 10, 5, 1), (6, 15, 14, 10, 35, 16, 15, 9, 1), (15, 60, 19, 15,
33, 12, 1), (20, 45, 14, 1), (15, 1), 1]
PROG
(SageMath)
def BellBlocks(n):
R = InfinitePolynomialRing(ZZ, 'v') # Thanks to F. Chapoton.
V = R.gen()
@cached_function
def T(n, k):
if k == 0: return V[0]^n
return sum(binomial(n-1, j-1)*V[j]*T(n-j, k-1) for j in (0..n-k+1))
P = (T(n, k) for k in (0..n))
return flatten([p.coefficients() for p in P])
for n in (0..8): print(BellBlocks(n))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, May 19 2020
STATUS
approved