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

1,5

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Index entries for sequences related to compositions

Formula

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

Example

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].

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

Crossrefs

Cf. A006141, A032020, A096401, A098133.

Sequence in context: A214079 A202742 A248771 * A339166 A359093 A291721

Adjacent sequences: A339443 A339444 A339445 * A339447 A339448 A339449

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2020

Status

approved