OFFSET
0,5
COMMENTS
The column o.g.f.s of this triangle appear as factors in the column o.g.f.s of triangle A008517 (second-order Eulerian numbers).
LINKS
FORMULA
G.f. column k: G(k, x):= x^(k-1)/product((1-j*x)^(k-j+1), j=1..k), k>=1.
a(n+k-1, k)=sum of product(binomial(n_j + k - 1, k - 1)*j^(n_j), j=1..k) with sum(n_j, j=1..k)=n, n_j >=0. There are binomial(n+k-1, k-1) terms of this sum and 1<=k<=n+1. a(n, k)=0 if n+1<k.
EXAMPLE
Rows: [1]; [1,1]; [1,4,1]; [1,11,10,1]; [1,26,60,20,1]; [1,57,282,225,35,1]; ...
a(4,3)= 60 = 6 + 12 + 9 + 12 + 9 + 12 from the binomial(4,2)=6 terms of the sum corresponding to (n_1,n_2,n_3) = (2,0,0), (0,2,0), (0,0,2), (1,1,0), (1,0,1) and (0,1,1).
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Oct 14 2005
STATUS
approved