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A339171
Number of compositions (ordered partitions) of n into distinct parts, the least being 8.
3
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
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]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 25 2020
STATUS
approved