A055586 Sixth column of triangle A055584.
1, 10, 59, 268, 1037, 3598, 11535, 34832, 100369, 278546, 749587, 1966100, 5046293, 12714006, 31522839, 77070360, 186122265, 444596250, 1051721755, 2466250780, 5737807901, 13254000670, 30417092639, 69390565408
Offset: 0
Links
- A. F. Y. Zhao, Pattern Popularity in Multiply Restricted Permutations, Journal of Integer Sequences, 17 (2014), #14.10.3.
- Index entries for linear recurrences with constant coefficients, signature (10,-41,88,-104,64,-16).
Programs
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Mathematica
CoefficientList[Series[1/(((1-x)^2)(1-2x)^4),{x,0,30}],x] (* or *) LinearRecurrence[{10,-41,88,-104,64,-16},{1,10,59,268,1037,3598},30] (* Harvey P. Dale, Jul 31 2025 *) -
PARI
Vec(1/(((1-x)^2)*(1-2*x)^4) + O(x^40)) \\ Michel Marcus, Dec 11 2015
Formula
G.f.: 1/(((1-x)^2)*(1-2*x)^4).
a(n) = A055584(n+5, 5).
a(n) = Sum_{j=0..n-1} a(j) + A055582(n) for n >= 1.
E.g.f.: exp(x)*(x + 9) + 8*exp(2*x)*(2*x^3 + 3*x^2 + 6*x - 3)/3. - Stefano Spezia, Sep 24 2024