A339108 Number of compositions (ordered partitions) of n into distinct parts >= 7.

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 17, 19, 25, 33, 39, 47, 59, 67, 79, 93, 129, 143, 185, 223, 289, 333, 423, 491, 611, 703, 847, 1089, 1281, 1547, 1889, 2323, 2833, 3417, 4095, 4967, 5939, 7099, 8359, 10653, 12345, 15047, 17993

Offset

0,16

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 + 13)/2) / Product_{j=1..k} (1 - x^j).

Example

a(15) = 3 because we have [15], [8, 7] and [7, 8].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-6)*(i+7)/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 = 60; CoefficientList[Series[Sum[k! x^(k (k + 13)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A017901, A025152, A032020, A032022, A185327, A339101, A339102, A339103, A339104, A339109, A339110.

Sequence in context: A339109 A237718 A245149 * A206914 A175298 A245148

Adjacent sequences: A339105 A339106 A339107 * A339109 A339110 A339111

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved