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A098992
Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324.
1
0, 0, 1, 11, 55, 190, 526, 1254, 2682, 5280, 9735, 17017, 28457, 45838, 71500, 108460, 160548, 232560, 330429, 461415, 634315, 859694, 1150138, 1520530, 1988350, 2574000, 3301155, 4197141, 5293341, 6625630, 8234840, 10167256, 12475144, 15217312, 18459705
OFFSET
1,4
FORMULA
G.f.: x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8.
From Colin Barker, Oct 26 2017: (Start)
a(n) = (n*(-540 + 476*n + 469*n^2 - 490*n^3 + 70*n^4 + 14*n^5 + n^6)) / 5040.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
PROG
(PARI) concat(vector(2), Vec(x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8 + O(x^30))) \\ Colin Barker, Oct 26 2017
CROSSREFS
Sequence in context: A226255 A022606 A072025 * A246990 A156589 A165791
KEYWORD
easy,nonn
AUTHOR
Mike Zabrocki, Nov 05 2004
STATUS
approved