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A241878 Number of ascent sequences of length n with exactly eight descents.

%I A241878 #11 May 07 2014 00:55:37
%S A241878 76,35209,4039194,242899690,9885744698,308499975033,7934181861432,
%T A241878 176105387674796,3481327075812644,62693622772259358,
%U A241878 1045913922174474652,16373263083718686437,242940967901333077989,3444033483761421576832,46951392190123945806932
%N A241878 Number of ascent sequences of length n with exactly eight descents.
%C A241878 Recurrence is of 52 order with constant coefficients (see link below).
%H A241878 Joerg Arndt and Alois P. Heinz, <a href="/A241878/b241878.txt">Table of n, a(n) for n = 13..1000</a>
%H A241878 Fung Lam, <a href="/A241878/a241878.txt">Recurrence formula for A241878</a>
%F A241878 G.f.: see Maple program.
%p A241878 gf:= -(52553412112007194214400000*x^39 -613289908725672396718080000*x^38 +3446340062218318299267072000*x^37 -12409743778368324350902272000*x^36 +32144544101639652703103877120*x^35 -63739623224842771994751467520*x^34 +100526156498120293361669455872*x^33 -129326381850884353971886854144*x^32 +138078181730156438217858923520*x^31 -123788362154790905517444399360*x^30
%p A241878 +93876678485180434126091194176*x^29 -60428403800498502691099934400*x^28 +32981578627042728537763538064*x^27 -15149960622696298673159858800*x^26 +5745076159441010911548301660*x^25 -1713942189473347432159782004*x^24 +344138671691755284367114047*x^23 -5839405428890160900553740*x^22
%p A241878 -32824622557763063660057790*x^21 +18176377898703093820133728*x^20 -6522560269430279741005099*x^19 +1814942458271772835455036*x^18 -411537276001965041120674*x^17 +77191887852380143515467*x^16 -11948748170525701008430*x^15 +1497118354975682972561*x^14
%p A241878 -144192168126331827895*x^13 +9057386760969303803*x^12 -33939433225045648*x^11 -78967551758852587*x^10 +11947165597637555*x^9 -1090933373158527*x^8 +69435729107323*x^7 -3048021102033*x^6 +80222524613*x^5 -392852647*x^4 -54444097*x^3 +1857643*x^2 -18717*x -76) *x^13 / ((10*x-1) *(9*x-1)^2 *(8*x-1)^3 *(7*x-1)^4 *(6*x-1)^5 *(5*x-1)^6 *(4*x-1)^7 *(x-1)^7 *(3*x-1)^8 *(2*x-1)^9):
%p A241878 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A241878 seq(a(n), n=13..30);
%Y A241878 Column k=8 of A238858.
%K A241878 nonn
%O A241878 13,1
%A A241878 _Joerg Arndt_ and _Alois P. Heinz_, Apr 30 2014