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A339446
Number of compositions (ordered partitions) of n into distinct parts such that the smallest part is equal to the number of parts.
2
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 05 2020
STATUS
approved