A339170 Number of compositions (ordered partitions) of n into distinct parts, the least being 7.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 32, 62, 62, 92, 116, 146, 170, 224, 248, 302, 350, 404, 572, 650, 818, 1016, 1328, 1526, 1958, 2300, 2852, 3314, 4010, 4592, 6248, 6974, 8750, 10436, 13196, 15722, 19442, 22952

Offset

0,16

Links

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

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=1} k! * x^(k*(k + 13)/2) / Product_{j=1..k-1} (1 - x^j).

Example

a(24) = 8 because we have [17, 7], [9, 8, 7], [9, 7, 8], [8, 9, 7], [8, 7, 9], [7, 17], [7, 9, 8] and [7, 8, 9].

Mathematica

nmax = 64; CoefficientList[Series[Sum[k! x^(k (k + 13)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026800, A026828, A339108, A339162, A339163, A339164, A339165, A339166, A339169, A339171, A339172.

Sequence in context: A244464 A250201 A252375 * A257773 A164898 A100801

Adjacent sequences: A339167 A339168 A339169 * A339171 A339172 A339173

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 25 2020

Status

approved