A339166 Number of compositions (ordered partitions) of n into distinct parts, the least being 5.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 56, 56, 86, 110, 140, 164, 218, 242, 296, 464, 518, 686, 884, 1172, 1370, 1802, 2120, 2672, 3134, 4526, 5108, 6764, 8186, 10682, 13088, 16544, 19790, 24950, 29876, 36716

Offset

0,12

Links

Table of n, a(n) for n=0..55.

Index entries for sequences related to compositions

Formula

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

Example

a(18) = 8 because we have [13, 5], [7, 6, 5], [7, 5, 6], [6, 7, 5], [6, 5, 7], [5, 13], [5, 7, 6] and [5, 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-> `if`(n<5, 0, b(n-5$2, 1)):
seq(a(n), n=0..60);  # Alois P. Heinz, Nov 25 2020

Mathematica

nmax = 55; CoefficientList[Series[Sum[k! x^(k (k + 9)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026798, A026826, A339103, A339162, A339163, A339164, A339165.

Sequence in context: A202742 A248771 A339446 * A359093 A291721 A109913

Adjacent sequences: A339163 A339164 A339165 * A339167 A339168 A339169

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 25 2020

Status

approved