A253207 a(n) = number of permutations of (1,2,...,n) producible by an ordered quadruple of distinct transpositions.

11, 59, 359, 1799, 7091, 22995, 64143, 159093, 359348, 752180, 1478204, 2754752, 4906202, 8402522, 13907394, 22337388, 34933761, 53348561, 79746821, 116926733, 168459797, 238853045, 333735545, 460071495, 626402322, 843120306, 1122776354

Offset

4,1

Links

Colin Barker, Table of n, a(n) for n = 4..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = n!*(1/(384*(n-8)!)+1/(24*(n-7)!)+13/(72*(n-6)!)+1/(5*(n-5)!)+1/(8*(n-4)!)+1/(3*(n-3)!)) for n>=8.

Prog

(PARI) Vec(-x^4*(2*x^8-18*x^7+72*x^6-168*x^5+254*x^4-232*x^3+224*x^2-40*x+11)/(x-1)^9 + O(x^100)) \\ Colin Barker, Dec 30 2014

Crossrefs

Cf. A000914, for two transpositions, and A253171, for three.

Sequence in context: A249891 A186256 A164299 * A241860 A082884 A193230

Adjacent sequences: A253204 A253205 A253206 * A253208 A253209 A253210

Keyword

nonn,easy

Author

Andrew Woods, Dec 28 2014

Status

approved