A241634 Number of compositions of n with exactly nine descents.

55, 856, 7752, 52203, 288439, 1377331, 5868260, 22792116, 81944050, 275852636, 877202199, 2653544633, 7679263550, 21360356057, 57331068005, 148970797526, 375812977280, 922708833921, 2209559805490, 5170203452802, 11840994145688, 26581854857244, 58569145064714

Offset: 27

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 = 27..1000

Crossrefs

Column k=9 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, 9):
seq(a(n), n=27..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, 9];
Table[a[n], {n, 27, 50}] (* Jean-François Alcover, Nov 28 2023, from Maple code *)