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A241876 Number of ascent sequences of length n with exactly six descents.

%I A241876 #8 May 07 2014 00:55:17
%S A241876 1,594,45747,1752513,45552389,920513763,15577569349,231095209005,
%T A241876 3098219351061,38346553035796,445033714399778,4900020726869918,
%U A241876 51649070462238267,524892382085986515,5172330086955870408,49648755377072570286,465988523060678103585
%N A241876 Number of ascent sequences of length n with exactly six descents.
%H A241876 Joerg Arndt and Alois P. Heinz, <a href="/A241876/b241876.txt">Table of n, a(n) for n = 10..1000</a>
%F A241876 G.f.: see Maple program.
%F A241876 Recurrence:
%F A241876 a(n) = 5056584744960000*a(n-33) - 68065242513408000*a(n-32) + 437803880015462400*a(n-31) - 1792719557254840320*a(n-30) + 5253036459825954816*a(n-29) - 11738495444617580544*a(n-28) + 20817456370349202432*a(n-27) - 30104829351014344704*a(n-26) + 36199103820290982144*a(n-25) - 36720645434814626560*a(n-24) + 31774115324102749056*a(n-23) - 23653530457275554304*a(n-22) + 15249527617274617248*a(n-21) - 8558081781076074864*a(n-20) + 4196991567155864940*a(n-19) - 1803694897653672920*a(n-18) + 680558169447265365*a(n-17) - 225674624312836065*a(n-16) + 65779879124624040*a(n-15) - 16842763995507000*a(n-14) + 3782553545656620*a(n-13) - 743262373360860*a(n-12) + 127338118210800*a(n-11) - 18930771191160*a(n-10) + 2426885862174*a(n-9) - 266102398566*a(n-8) + 24690049848*a(n-7) - 1911283016*a(n-6) + 121101516*a(n-5) - 6114540*a(n-4) + 236484*a(n-3) - 6576*a(n-2) + 117*a(n-1). - _Fung Lam_, May 06 2014
%p A241876 gf:= -(57480192000000*x^23 -445890272256000*x^22+1619423860193280*x^21 -3652404812826624*x^20 +5721231909570048*x^19 -6594644113079904*x^18 +5779639610824024*x^17 -3921044317402316*x^16 +2072911198114226*x^15 -849438228561495*x^14 +263329934846856*x^13 -57503572316263*x^12
%p A241876 +6610760803436*x^11 +737845435920*x^10 -563506749299*x^9 +146999655366*x^8 -24201211392*x^7 +2687528742*x^6 -192088566*x^5 +6983684*x^4 +69774*x^3 -17175*x^2 +477*x+1) *x^10 / ((8*x-1) *(7*x-1)^2 *(6*x-1)^3 *(5*x-1)^4 *(4*x-1)^5 *(x-1)^5 *(3*x-1)^6 *(2*x-1)^7):
%p A241876 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A241876 seq(a(n), n=10..30);
%Y A241876 Column k=6 of A238858.
%K A241876 nonn
%O A241876 10,2
%A A241876 _Joerg Arndt_ and _Alois P. Heinz_, Apr 30 2014