A339171 Number of compositions (ordered partitions) of n into distinct parts, the least being 8.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 32, 38, 62, 68, 92, 122, 146, 176, 224, 254, 302, 356, 404, 458, 650, 704, 896, 1094, 1406, 1604, 2060, 2378, 2954, 3416, 4112, 4694, 5654, 7076, 8156, 9842

Offset

0,18

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=1} k! * x^(k*(k + 15)/2) / Product_{j=1..k-1} (1 - x^j).

Example

a(27) = 8 because we have [19, 8], [10, 9, 8], [10, 8, 9], [9, 10, 8], [9, 8, 10], [8, 19], [8, 10, 9] and [8, 9, 10].

Mathematica

nmax = 65; CoefficientList[Series[Sum[k! x^(k (k + 15)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026801, A026829, A339109, A339162, A339163, A339164, A339165, A339166, A339169, A339170, A339172.

Sequence in context: A103378 A103663 A349925 * A083311 A104230 A226774

Adjacent sequences: A339168 A339169 A339170 * A339172 A339173 A339174

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 25 2020

Status

approved