A339110 Number of compositions (ordered partitions) of n into distinct parts >= 9.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 19, 21, 27, 35, 41, 49, 61, 69, 81, 95, 107, 121, 163, 177, 219, 263, 329, 373, 469, 537, 657, 755, 899, 1021, 1219, 1485, 1707, 2027, 2417, 2881, 3445, 4077, 4809, 5735, 6755, 7969, 9307

Offset

0,20

Links

Table of n, a(n) for n=0..66.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 17)/2) / Product_{j=1..k} (1 - x^j).

Example

a(19) = 3 because we have [19], [10, 9] and [9, 10].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-8)*(i+9)/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..69);  # Alois P. Heinz, Nov 23 2020

Mathematica

nmax = 66; CoefficientList[Series[Sum[k! x^(k (k + 17)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A017903, A025154, A032020, A032022, A185329, A339101, A339102, A339103, A339104, A339108, A339109.

Sequence in context: A109613 A063196 A351744 * A245150 A339109 A237718

Adjacent sequences: A339107 A339108 A339109 * A339111 A339112 A339113

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved