A326963 Number of length n arrays with entries that cover an initial interval of positive integers counting chiral pairs as equivalent, i.e., the arrays are reversible.

1, 1, 2, 8, 39, 277, 2348, 23684, 272955, 3543901, 51124052, 811318628, 14045786139, 263429197837, 5320671508868, 115141595761844, 2657827341263595, 65185383518111581, 1692767331631966292, 46400793659715329348, 1338843898122243225339, 40562412499252848257197

Offset: 0

Author

Andrew Howroyd, Sep 13 2019

Keywords

• nonn

Examples

			a(3) = 8 because there are the following arrays up to reversal:
   111,
   112, 121, 122, 212,
   123, 132, 213.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Row sums of A305621.

Programs

PARI

a(n) = {sum(k=0, n, k! * (stirling(n, k, 2) + stirling((n+1)\2, k, 2)) / 2)}

Formula

a(n) = Sum_{k=0..n} (k!/2) * (Stirling2(n, k) + Stirling2(ceiling(n/2), k)).