[seqfans] A038719 formula
pin
pin at myway.com
Mon Jul 21 22:43:28 CEST 2003
Hello seqfans,
Would someone please be so kind as to check up the following formula as it appears in the entry A038719:
Name: Triangle T(n,k) (0<=k<=n) giving number of chains of length k in partially ordered set formed from subsets of n-set by inclusion.
References R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64(1991), 23-31.
Formula: T(n,k) = Sum_{j=0..k} (_1)^j*C(n,k)*(k+2-j)^n.
Example: 1; 2,1; 4,5,2; 8,19,18,6; 16,65,110,84,24; ...
If C(.,.) is the binomial coefficient, and (_1) is a typo for (-1), then I am not getting the actual triangle listed.
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