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

0,3

Links

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

Formula

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

Example

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

Prog

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

Crossrefs

Row sums of A305621.

Sequence in context: A217945 A091073 A266468 * A306781 A154132 A152458

Adjacent sequences: A326960 A326961 A326962 * A326964 A326965 A326966

Keyword

nonn

Author

Andrew Howroyd, Sep 13 2019

Status

approved