A339103 Number of compositions (ordered partitions) of n into distinct parts >= 5.

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 15, 17, 23, 31, 37, 45, 57, 65, 101, 115, 151, 189, 255, 293, 383, 451, 565, 777, 921, 1157, 1469, 1855, 2311, 2865, 3495, 4313, 5231, 7063, 8269, 10509, 12849, 16217, 19829, 25171, 30031, 37485, 45183

Offset

0,12

Links

Table of n, a(n) for n=0..54.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 9)/2) / Product_{j=1..k} (1 - x^j).

Example

a(11) = 3 because we have [11], [6, 5] and [5, 6].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-4)*(i+5)/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 = 54; CoefficientList[Series[Sum[k! x^(k (k + 9)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A017899, A025150, A032020, A032022, A185325, A339101, A339102, A339104.

Sequence in context: A073737 A237716 A245147 * A187072 A133908 A111213

Adjacent sequences: A339100 A339101 A339102 * A339104 A339105 A339106

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved