A241633 Number of compositions of n with exactly eight descents.

34, 474, 3914, 24222, 123713, 548540, 2178219, 7909965, 26662725, 84357961, 252677505, 721404913, 1974020281, 5200561960, 13240895310, 32684520969, 78435463950, 183422986603, 418849888662, 935640152746, 2047838246581, 4397763452093, 9278220501698

Offset

24,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 24..1000

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j<i, x, 1), j=1..n), x, 9), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 8):
seq(a(n), n=24..50);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*
   If[j < i, x, 1], {j, 1, n}] // Expand];
a[n_] := Coefficient[b[n, 0], x, 8];
Table[a[n], {n, 24, 50}] (* Jean-François Alcover, Nov 28 2023, from Maple code *)

Crossrefs

Column k=8 of A238343 and of A238344.

Sequence in context: A244495 A107917 A277226 * A302383 A303104 A066291

Adjacent sequences: A241630 A241631 A241632 * A241634 A241635 A241636

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved