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A339163 Number of compositions (ordered partitions) of n into distinct parts, the least being 2. 8
0, 0, 1, 0, 0, 2, 2, 2, 2, 8, 8, 14, 14, 20, 44, 50, 74, 104, 128, 158, 326, 356, 524, 698, 986, 1160, 1592, 2606, 3158, 4316, 5708, 7706, 10082, 12920, 16136, 25718, 30614, 41756, 53396, 71978, 91058, 122144, 149384, 193670, 279614, 342860, 447764, 581234 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
FORMULA
G.f.: Sum_{k>=1} k! * x^(k*(k + 3)/2) / Product_{j=1..k-1} (1 - x^j).
EXAMPLE
a(9) = 8 because we have [7, 2], [4, 3, 2], [4, 2, 3], [3, 4, 2], [3, 2, 4], [2, 7], [2, 4, 3] and [2, 3, 4].
MAPLE
b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-2)*(i+3)/2<n, 0,
add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<2, 0, b(n-2$2, 1)):
seq(a(n), n=0..55); # Alois P. Heinz, Nov 25 2020
MATHEMATICA
nmax = 47; CoefficientList[Series[Sum[k! x^(k (k + 3)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A013598 A100943 A152660 * A058787 A353392 A360310
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 25 2020
STATUS
approved

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)