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A095889 Number of permutations of [n] with exactly 3 descents which avoid the pattern 4321. 1
10, 148, 1260, 8160, 44790, 220180, 1001000, 4295168, 17633122, 69921460, 269652100, 1016524352, 3760334958, 13690636212, 49172875520, 174559419680, 613383654170, 2136135472020, 7380351046300, 25319087913760, 86308819112550, 292526411823828, 986294675689560 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 19:46 EDT 2021. Contains 348044 sequences. (Running on oeis4.)