A339101 Number of compositions (ordered partitions) of n into distinct parts >= 3.

1, 0, 0, 1, 1, 1, 1, 3, 3, 5, 5, 7, 13, 15, 21, 29, 35, 43, 79, 87, 123, 161, 221, 259, 349, 531, 645, 857, 1115, 1471, 1903, 2403, 2979, 4493, 5357, 7135, 9013, 11919, 14925, 19685, 23939, 30667, 42679, 52215, 67035, 86009, 109541, 137923, 177493, 222027, 277749

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 5)/2) / Product_{j=1..k} (1 - x^j).

Example

a(7) = 3 because we have [7], [4, 3] and [3, 4].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-2)*(i+3)/2<n, 0, add(
         b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50);  # Alois P. Heinz, Nov 23 2020

Mathematica

nmax = 50; CoefficientList[Series[Sum[k! x^(k (k + 5)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A008483, A025148, A032020, A032022, A078012, A339102, A339103, A339104.

Sequence in context: A245145 A092316 A327710 * A142456 A098508 A355572

Adjacent sequences: A339098 A339099 A339100 * A339102 A339103 A339104

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved