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

Author

Andrew Woods, Dec 28 2014

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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

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.