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Expansion of x^5*(1 - x)^2*(4 - 14*x + 8*x^2 + 11*x^3 - 6*x^4 - 2*x^5 + 2*x^6 + 5*x^7 - 2*x^8 + x^9)/(1 - 2*x)^4.
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%I #28 Jun 16 2015 10:57:28

%S 0,0,0,0,0,4,10,24,61,148,349,808,1847,4174,9346,20764,45825,100552,

%T 219528,477152,1033008,2228480,4792064,10274816,21972224,46872576,

%U 99768320,211918848,449277952,950796288,2008809472,4237557760,8926068736,18776326144

%N Expansion of x^5*(1 - x)^2*(4 - 14*x + 8*x^2 + 11*x^3 - 6*x^4 - 2*x^5 + 2*x^6 + 5*x^7 - 2*x^8 + x^9)/(1 - 2*x)^4.

%H Bruno Berselli, <a href="/A212330/b212330.txt">Table of n, a(n) for n = 0..1000</a>

%H Toufik Mansour, Sherry H. F. Yan and Laura L. M. Yang, <a href="http://www.math.ualberta.ca/~lyang/Papers/231-involution.pdf">Counting occurrences of 231 in an involution</a>, Discrete Mathematics 306 (2006), pages 564-572 (see Corollary 3.5, first case).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).

%F G.f.: x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4.

%F For n>12, a(n) = 2^(n-17)*(n^3+414*n^2+12227*n-30762)/3.

%F a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) for n>16, n=4, n=11.

%t CoefficientList[Series[x^5 (1 - x)^2 (4 - 14 x + 8 x^2 + 11 x^3 - 6 x^4 - 2 x^5 + 2 x^6 + 5 x^7 - 2 x^8 + x^9)/(1 - 2 x)^4, {x, 0, 34}], x]

%o (PARI) Vec(x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4+O(x^34)) \\ show terms starting with 4.

%o (Maxima) makelist(coeff(taylor(x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4, x, 0, n), x, n), n, 0, 33);

%Y Cf. A192886.

%K nonn,easy

%O 0,6

%A _Bruno Berselli_, May 28 2012