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

Author

Ilya Gutkovskiy, Nov 25 2020

Keywords

• nonn

Examples

			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].
		

Links

• Index entries for sequences related to compositions

Crossrefs

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

Programs

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]

Formula

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