A339109 Number of compositions (ordered partitions) of n into distinct parts >= 8.

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 19, 19, 27, 33, 41, 47, 61, 67, 81, 93, 107, 143, 163, 199, 243, 309, 353, 443, 517, 631, 729, 873, 995, 1307, 1459, 1795, 2115, 2625, 3089, 3767, 4405, 5371, 6297, 7557, 8771, 10463, 12811, 14911

Offset

0,18

Links

Table of n, a(n) for n=0..64.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 15)/2) / Product_{j=1..k} (1 - x^j).

Example

a(17) = 3 because we have [17], [9, 8] and [8, 9].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-7)*(i+8)/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..64);  # Alois P. Heinz, Nov 23 2020

Mathematica

nmax = 64; CoefficientList[Series[Sum[k! x^(k (k + 15)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A017902, A025153, A032020, A032022, A185328, A339101, A339102, A339103, A339104, A339108, A339110.

Sequence in context: A351744 A339110 A245150 * A237718 A245149 A339108

Adjacent sequences: A339106 A339107 A339108 * A339110 A339111 A339112

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved