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A241873 Number of ascent sequences of length n with exactly three descents.

%I A241873 #22 Jul 14 2015 11:11:05
%S A241873 1,48,822,9305,83590,647891,4537169,29532566,182034751,1076357002,
%T A241873 6162251432,34394051095,188121970788,1012370499109,5376927101387,
%U A241873 28254655805724,147182871736245,761235618312420,3914066453608570,20027841005048805,102071452026321906
%N A241873 Number of ascent sequences of length n with exactly three descents.
%H A241873 Joerg Arndt and Alois P. Heinz, <a href="/A241873/b241873.txt">Table of n, a(n) for n = 6..1000</a>
%H A241873 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (32,-461,3952,-22443,88896,-251663,512656,-745096,752672,-500976,196992,-34560).
%F A241873 G.f.: -(912*x^6-2440*x^5+2481*x^4-1177*x^3+253*x^2-16*x-1)*x^6 / ((5*x-1) *(4*x-1)^2 *(x-1)^2 *(3*x-1)^3 *(2*x-1)^4).
%F A241873 a(n) = 3*5^(n-1)/8 - 4^(n-1)*n/3 + 3^(n-2)*(6*n^2-2*n-7)/16 - 2^(n-5)*(n-2)*(n-1)*(n+3)/3 - n/24 + 1/16. - _Vaclav Kotesovec_, May 03 2014
%F A241873 Recurrence: a(n) = -34560*a(n-12) + 196992*a(n-11) - 500976*a(n-10) + 752672*a(n-9) - 745096*a(n-8) + 512656*a(n-7) - 251663*a(n-6) + 88896*a(n-5) - 22443*a(n-4) + 3952*a(n-3) - 461*a(n-2) + 32*a(n-1). - _Fung Lam_, May 05 2014
%p A241873 gf:= -(912*x^6-2440*x^5+2481*x^4-1177*x^3+253*x^2-16*x-1)*x^6/
%p A241873       ((5*x-1)*(4*x-1)^2*(x-1)^2*(3*x-1)^3*(2*x-1)^4):
%p A241873 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A241873 seq(a(n), n=6..30);
%t A241873 CoefficientList[Series[-(912 x^6 - 2440 x^5 + 2481 x^4 - 1177 x^3 + 253 x^2 - 16 x - 1)/((5 x - 1) (4 x - 1)^2 (x - 1)^2 (3 x - 1)^3 (2 x - 1)^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 06 2014 *)
%t A241873 LinearRecurrence[{32,-461,3952,-22443,88896,-251663,512656,-745096,752672,-500976,196992,-34560},{1,48,822,9305,83590,647891,4537169,29532566,182034751,1076357002,6162251432,34394051095},21] (* _Ray Chandler_, Jul 14 2015 *)
%Y A241873 Column k=3 of A238858.
%K A241873 nonn,easy
%O A241873 6,2
%A A241873 _Joerg Arndt_ and _Alois P. Heinz_, Apr 30 2014