A339446 Number of compositions (ordered partitions) of n into distinct parts such that the smallest part is equal to the number of parts.

1, 0, 0, 0, 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, 452, 530, 698, 776, 968, 1166, 1478, 1700, 2132, 2474, 3050, 3512, 4208, 4814, 5750, 6476, 7556, 8522, 10562, 11672, 13952, 16022, 19286, 22316, 26540

Offset: 1

Author

Ilya Gutkovskiy, Dec 05 2020

Keywords

• nonn

Examples

			a(12) = 8 because we have [10, 2], [2, 10], [5, 4, 3], [5, 3, 4], [4, 5, 3], [4, 3, 5], [3, 5, 4] and [3, 4, 5].
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to compositions

Crossrefs

Cf. A006141, A032020, A096401, A098133.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[k! x^(k (3 k - 1)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} k! * x^(k*(3*k - 1)/2) / Product_{j=1..k-1} (1 - x^j).