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

27,1

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 27..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, 10), polynom))
    end:
a:= n-> 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 *)

Crossrefs

Column k=9 of A238343 and of A238344.

Sequence in context: A297523 A221786 A358634 * A008402 A281073 A329753

Adjacent sequences: A241631 A241632 A241633 * A241635 A241636 A241637

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Status

approved