A151578 Number of permutations of 1..n arranged in a circle with exactly 5 adjacent element pairs in decreasing order.

0, 6, 399, 9528, 140571, 1561900, 14413894, 116857368, 862140162, 5925941490, 38576132625, 240659672336, 1451515055333, 8520359419080, 48925419854400, 275923203690000, 1533178869210324, 8414851432723230, 45712442315346915, 246193095207323400, 1316311515774609375

Offset

5,2

Links

Andrew Howroyd, Table of n, a(n) for n = 5..500

Formula

From Andrew Howroyd, May 05 2020: (Start)

a(n) = n*A000505(n-1).

a(n) = n*(5^(n-1) - n*4^(n-1) + binomial(n,2)*3^(n-1) - binomial(n,3)*2^(n-1) + binomial(n,4)). (End)

Prog

(PARI) a(n) = {n*(5^(n-1) - n*4^(n-1) + binomial(n, 2)*3^(n-1) - binomial(n, 3)*2^(n-1) + binomial(n, 4))} \\ Andrew Howroyd, May 05 2020

Crossrefs

Column k=5 of A334218.

Cf. A000505.

Sequence in context: A000474 A291593 A029591 * A172227 A331352 A159015

Adjacent sequences: A151575 A151576 A151577 * A151579 A151580 A151581

Keyword

nonn

Author

R. H. Hardin, May 21 2009

Extensions

Terms a(17) and beyond from Andrew Howroyd, May 05 2020

Status

approved