A241630 Number of compositions of n with exactly five descents.

8, 73, 429, 1945, 7465, 25317, 78068, 222963, 597644, 1518370, 3683950, 8586866, 19320391, 42127208, 89307361, 184578961, 372786467, 737212357, 1429992711, 2724852920, 5107392644, 9427895421, 17157142969, 30810379849, 54643242181, 95783964110, 166059755226

Offset: 15

Author

Joerg Arndt and Alois P. Heinz, Apr 26 2014

Keywords

• nonn

Examples

			a(15) = 8: [3,2,1,2,1,3,2,1], [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], [2,1,3,2,1,2,1,2,1], [3,2,1,2,1,2,1,2,1], [2,1,2,1,2,1,3,2,1], [2,1,2,1,2,1,2,1,2,1].
		

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 15..1000

Crossrefs

Column k=5 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, 5):
seq(a(n), n=15..50);

Mathematica

k = 5;
b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n - j, j]*
     If[j < i, x, 1], {j, n}] + O[x]^(k + 1)];
a[n_] := SeriesCoefficient[b[n, 0], {x, 0, k}];
a /@ Range[15, 50] (* Jean-François Alcover, Aug 27 2021, after Maple code *)