A241632 Number of compositions of n with exactly seven descents.

21, 259, 1932, 10898, 51083, 208936, 768594, 2594957, 8158005, 24140097, 67794864, 181889780, 468678716, 1164905882, 2803070038, 6549961919, 14901997455, 33085162997, 71822232573, 152710556875, 318509850193, 652536555773, 1314728710475, 2607856668543

Offset: 21

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Keywords

• nonn

Examples

			a(21) = 21: [3,2,1,2,1,3,2,1,3,2,1], [3,2,1,3,2,1,2,1,3,2,1], [3,2,1,3,2,1,3,2,1,2,1], [2,1,3,2,1,3,2,1,3,2,1], [2,1,2,1,2,1,3,2,1,3,2,1], [3,2,1,3,2,1,2,1,2,1,2,1], [2,1,2,1,3,2,1,2,1,3,2,1], [2,1,3,2,1,2,1,3,2,1,2,1], [3,2,1,2,1,3,2,1,2,1,2,1], [3,2,1,2,1,2,1,2,1,3,2,1], [2,1,3,2,1,2,1,2,1,3,2,1], [3,2,1,2,1,2,1,3,2,1,2,1], [2,1,2,1,3,2,1,3,2,1,2,1], [2,1,3,2,1,3,2,1,2,1,2,1], [3,2,1,2,1,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,2,1,3,2,1], [2,1,3,2,1,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,3,2,1,2,1], [2,1,2,1,2,1,3,2,1,2,1,2,1], [2,1,2,1,3,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,2,1,2,1,2,1,2,1].
		

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 21..1000

Crossrefs

Column k=7 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, 7):
seq(a(n), n=21..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, 7];
Table[a[n], {n, 21, 50}] (* Jean-François Alcover, Nov 28 2023, from Maple code *)