A339104 Number of compositions (ordered partitions) of n into distinct parts >= 6.

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 17, 17, 25, 31, 39, 45, 59, 65, 79, 115, 129, 165, 209, 269, 313, 403, 471, 585, 683, 941, 1063, 1375, 1641, 2097, 2537, 3161, 3745, 4663, 5535, 6741, 8627, 10241, 12535, 15307, 18849, 22869, 28409

Offset

0,14

Links

Table of n, a(n) for n=0..57.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 11)/2) / Product_{j=1..k} (1 - x^j).

Example

a(13) = 3 because we have [13], [7, 6] and [6, 7].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-5)*(i+6)/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..60);  # Alois P. Heinz, Nov 23 2020

Mathematica

nmax = 57; CoefficientList[Series[Sum[k! x^(k (k + 11)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A017900, A025151, A032020, A032022, A185326, A339101, A339102, A339103.

Sequence in context: A206914 A175298 A245148 * A073737 A237716 A245147

Adjacent sequences: A339101 A339102 A339103 * A339105 A339106 A339107

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved