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A339162 Number of compositions (ordered partitions) of n into distinct parts, the least being 1. 8
0, 1, 0, 2, 2, 2, 8, 8, 14, 14, 44, 44, 74, 98, 128, 272, 326, 470, 644, 932, 1106, 2234, 2552, 3800, 4958, 7070, 9068, 12140, 20042, 24674, 34256, 45632, 61814, 80630, 109316, 135572, 217778, 262298, 362744, 466664, 636494, 805454, 1085804, 1375388, 1776938, 2591762 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
G.f.: Sum_{k>=1} k! * x^(k*(k + 1)/2) / Product_{j=1..k-1} (1 - x^j).
EXAMPLE
a(6) = 8 because we have [5, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 5], [1, 3, 2] and [1, 2, 3].
MAPLE
b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-1)*(i+2)/2<n, 0,
add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<1, 0, b(n-1$2, 1)):
seq(a(n), n=0..55); # Alois P. Heinz, Nov 25 2020
MATHEMATICA
nmax = 45; CoefficientList[Series[Sum[k! x^(k (k + 1)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A353245 A275928 A221072 * A360808 A168272 A222448
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.)