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A375838
Number of rooted chains starting with the cycle (1)(2)(3)...(n) in the permutation poset of [n].
1
1, 1, 2, 9, 83, 1270, 28799, 906899, 37866842, 2024422837, 134850653405, 10950546880152, 1064840930492393, 122158078221727119, 16325324374155336370, 2514183676808883419043, 442023695390488997377405, 87989953715757624724243004, 19688099473681895327628896249, 4919839221134662388853128069571, 1365091729320293490230304687026514
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} A375837(n,k).
a(n) = (A375836(n)+1)/2.
EXAMPLE
Consider the set S = {1, 2, 3}. The a(3) = 1 + 5 + 3 = 9 in the poset of permutations of {1,2,3}:
|{(1)(2)(3)}| = 1;
|{(1)(2)(3) < (1)(23), (1)(2)(3) < (2)(13), (1)(2)(3) < (3)(12), (1)(2)(3) < (123), (1)(2)(3) < (132)}|=5;
|{(1)(2)(3) < (1)(23) < (123), (1)(2)(3) < (2)(13)< (132), (1)(2)(3) < (3)(12) < (123)}| = 3.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rajesh Kumar Mohapatra, Subhashree Sahoo, and Ranjan Kumar Dhani, Sep 10 2024
STATUS
approved