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

8,1

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).

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

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 *)

Crossrefs

Column k=4 of A238858.

Sequence in context: A241871 A160261 A357376 * A330497 A037138 A091429

Adjacent sequences: A241871 A241872 A241873 * A241875 A241876 A241877

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved