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A241875 Number of ascent sequences of length n with exactly five descents.

%I A241875 #12 May 07 2014 00:55:09
%S A241875 8,937,35841,834115,14475124,206587438,2564426795,28685171369,
%T A241875 296140258017,2869968329846,26436819147050,233659504323986,
%U A241875 1995996397796603,16573895612885901,134389245968036082,1068038768762441634,8344630999626596958,64255565358244018191
%N A241875 Number of ascent sequences of length n with exactly five descents.
%H A241875 Joerg Arndt and Alois P. Heinz, <a href="/A241875/b241875.txt">Table of n, a(n) for n = 9..1000</a>
%F A241875 G.f.: see Maple program.
%F A241875 Recurrence: a(n) = 81*a(n-1) - 3114*a(n-2) + 75618*a(n-3) - 1302183*a(n-4)  + 16924743*a(n-5) - 172522788*a(n-6) + 1414869228*a(n-7) - 9501687423*a(n-8) + 52906702383*a(n-9) - 246402134298*a(n-10) + 965539475298*a(n-11) - 3194875953273*a(n-12) + 8941122759033*a(n-13) - 21157696301688*a(n-14) + 42243068089008*a(n-15) - 70868692309248*a(n-16) + 99257760429408*a(n-17) - 114988409883008*a(n-18) + 108762502457088*a(n-19) - 82478130147072*a(n-20)  + 48857688836352*a(n-21) - 21745388335104*a(n-22) + 6829114613760*a(n-23) - 1347275980800*a(n-24) + 125411328000*a(n-25). - _Fung Lam_, May 05 2014
%p A241875 gf:= -(1789516800*x^16 -10641300480*x^15 +28799118720*x^14 -46828104768*x^13 +50870603132*x^12 -38817852028*x^11 +21260210219*x^10 -8353318594*x^9 +2286195777*x^8 -394486012*x^7 +25511399*x^6 +6059293*x^5 -1915919*x^4 +243868*x^3 -15144*x^2 +289*x+8) *x^9 / ((7*x-1) *(6*x-1)^2 *(5*x-1)^3 *(4*x-1)^4 *(x-1)^4 *(3*x-1)^5 *(2*x-1)^6):
%p A241875 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A241875 seq(a(n), n=9..30);
%t A241875 CoefficientList[Series[-(1789516800 x^16 - 10641300480 x^15 + 28799118720 x^14 - 46828104768 x^13 + 50870603132 x^12 - 38817852028 x^11 + 21260210219 x^10 - 8353318594 * x^9 + 2286195777 * x^8 - 394486012 * x^7 + 25511399 x^6 + 6059293 x^5 - 1915919 x^4 + 243868 x^3 - 15144 x^2 + 289 x + 8)/((7 x - 1) (6 x - 1)^2 (5 x - 1)^3 (4 x - 1)^4 (x - 1)^4 (3 x - 1)^5 (2 x - 1)^6), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 06 2014 *)
%Y A241875 Column k=5 of A238858.
%K A241875 nonn
%O A241875 9,1
%A A241875 _Joerg Arndt_ and _Alois P. Heinz_, Apr 30 2014