A241874 Number of ascent sequences of length n with exactly four descents.

26, 1048, 21362, 307660, 3574869, 35900857, 324623778, 2713846040, 21359949568, 160346402882, 1159100542422, 8127076433744, 55581620321035, 372410647606299, 2453173612562310, 15932182184914620, 102249194946464430, 649680545407603980, 4093272335570479850

Offset: 8

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Keywords

• nonn

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..1000
• Index entries for linear recurrences with constant coefficients, signature(53, -1308, 19968, -211254, 1644366, -9756556, 45104276, -164641137, 477888789, -1105173264, 2030572644, -2940614560, 3309217712, -2828604672, 1770962112, -764322048, 202798080, -24883200).

Crossrefs

Column k=4 of A238858.

Programs

Maple

gf:= -(466560*x^10 -1981728*x^9 +3631752*x^8 -3741230*x^7 +2365035*x^6 -936340*x^5 +223475*x^4 -27090*x^3 +174*x^2 +330*x -26) *x^8 / ((6*x-1) *(5*x-1)^2 *(4*x-1)^3 *(x-1)^3 *(3*x-1)^4 *(2*x-1)^5):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=8..30);

Mathematica

CoefficientList[Series[-(466560 x^10 - 1981728 x^9 + 3631752 x^8 - 3741230 x^7 + 2365035 x^6 - 936340 x^5 + 223475 x^4 - 27090 x^3 + 174 x^2 + 330 x - 26)/((6 x - 1) (5 x - 1)^2 (4 x - 1)^3 (x - 1)^3 (3 x - 1)^4 (2 x - 1)^5), {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2014 *)
LinearRecurrence[{53, -1308, 19968, -211254, 1644366, -9756556, 45104276, -164641137, 477888789, -1105173264, 2030572644, -2940614560, 3309217712, -2828604672, 1770962112, -764322048, 202798080, -24883200},{26, 1048, 21362, 307660, 3574869, 35900857, 324623778, 2713846040, 21359949568, 160346402882, 1159100542422, 8127076433744, 55581620321035, 372410647606299, 2453173612562310, 15932182184914620, 102249194946464430, 649680545407603980}, 20];(* Ray Chandler, Jul 15 2015 *)

Formula

G.f.: -(466560*x^10 -1981728*x^9 +3631752*x^8 -3741230*x^7 +2365035*x^6 -936340*x^5 +223475*x^4 -27090*x^3 +174*x^2 +330*x -26) *x^8 / ((6*x-1) *(5*x-1)^2 *(4*x-1)^3 *(x-1)^3 *(3*x-1)^4 *(2*x-1)^5).

Recurrence: a(n) = - 24883200*a(n-18) + 202798080*a(n-17) - 764322048*a(n-16) + 1770962112*a(n-15) - 2828604672*a(n-14) + 3309217712*a(n-13) - 2940614560*a(n-12) + 2030572644*a(n-11) - 1105173264*a(n-10) + 477888789*a(n-9) - 164641137*a(n-8) + 45104276*a(n-7) - 9756556*a(n-6) + 1644366*a(n-5) - 211254*a(n-4) + 19968*a(n-3) - 1308*a(n-2) + 53*a(n-1). - Fung Lam, May 05 2014