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A339172
Number of compositions (ordered partitions) of n into distinct parts, the least being 9.
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 32, 38, 38, 68, 68, 98, 122, 152, 176, 230, 254, 308, 356, 410, 458, 536, 704, 782, 974, 1172, 1484, 1706, 2138, 2480, 3056, 3518, 4214, 4820, 5756
OFFSET
0,20
FORMULA
G.f.: Sum_{k>=1} k! * x^(k*(k + 17)/2) / Product_{j=1..k-1} (1 - x^j).
EXAMPLE
a(30) = 8 because we have [21, 9], [11, 10, 9], [11, 9, 10], [10, 11, 9], [10, 9, 11], [9, 21], [9, 11, 10] and [9, 10, 11].
MATHEMATICA
nmax = 67; CoefficientList[Series[Sum[k! x^(k (k + 17)/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