A241635 Number of compositions of n with exactly ten descents.

89, 1529, 15072, 109700, 651755, 3333143, 15159290, 62673818, 239267852, 853417204, 2869778022, 9163554647, 27947044811, 81799126374, 230699706092, 629085587197, 1663426352840, 4275866388599, 10708451601656, 26178837135330, 62580214195713, 146503017803381

Offset: 30

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 = 30..1000

Crossrefs

Column k=10 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, 10):
seq(a(n), n=30..55);

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, 10];
Table[a[n], {n, 30, 55}] (* Jean-François Alcover, Nov 28 2023, from Maple code *)