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

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=8 of A238343 and of A238344.

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, convert(series(add(b(n-j, j)*
      `if`(j 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 *)