A095889 Number of permutations of [n] with exactly 3 descents which avoid the pattern 4321.

10, 148, 1260, 8160, 44790, 220180, 1001000, 4295168, 17633122, 69921460, 269652100, 1016524352, 3760334958, 13690636212, 49172875520, 174559419680, 613383654170, 2136135472020, 7380351046300, 25319087913760, 86308819112550, 292526411823828, 986294675689560

Offset

5,1

Links

Colin Barker, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (22,-216,1248,-4710,12180,-22004,27752,-23937,13446,-4428,648).

Formula

G.f.: 2*x^5*(5 - 36*x + 82*x^2 - 36*x^3 - 87*x^4 + 80*x^5) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^4).

a(n) = (n*(27 + 81*2^n - 115*3^n + 3*(27*2^n+2*3^n)*n + (-27+3^n)*n^2)) / 162. - Colin Barker, May 03 2019

Prog

(PARI) Vec(2*x^5*(5 - 36*x + 82*x^2 - 36*x^3 - 87*x^4 + 80*x^5) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^4) + O(x^30)) \\ Colin Barker, Nov 03 2017

Crossrefs

Cf. A000295, A000460.

Sequence in context: A297714 A055761 A295524 * A097638 A178084 A098270

Adjacent sequences: A095886 A095887 A095888 * A095890 A095891 A095892

Keyword

nonn,easy

Author

Mike Zabrocki, Nov 10 2004

Status

approved