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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

(list; graph; refs; listen; history; text; internal format)

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