A098995 Number of permutations of [n] with exactly 4 descents which avoid the pattern 1324.
0, 0, 0, 0, 1, 57, 812, 6524, 37309, 169298, 648216, 2176923, 6582869, 18262399, 47129249, 114344261, 262987603, 577216181, 1215552037, 2467076907, 4843870146, 9229556242, 17113017451, 30949065535, 54705281270, 94677736245, 160689668475, 267828562140, 438931138500
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
Programs
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PARI
concat(vector(4), Vec(x^5*(1 + 40*x - 21*x^2 - 208*x^3 + 453*x^4 - 379*x^5 + 74*x^6 + 107*x^7 - 92*x^8 + 30*x^9 - 4*x^10) / (1 - x)^17 + O(x^30))) \\ Colin Barker, Nov 03 2017
Formula
G.f.: x^5*(1 + 40*x - 21*x^2 - 208*x^3 + 453*x^4 - 379*x^5 + 74*x^6 + 107*x^7 - 92*x^8 + 30*x^9 - 4*x^10) / (1 - x)^17.