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A339101
Number of compositions (ordered partitions) of n into distinct parts >= 3.
8
1, 0, 0, 1, 1, 1, 1, 3, 3, 5, 5, 7, 13, 15, 21, 29, 35, 43, 79, 87, 123, 161, 221, 259, 349, 531, 645, 857, 1115, 1471, 1903, 2403, 2979, 4493, 5357, 7135, 9013, 11919, 14925, 19685, 23939, 30667, 42679, 52215, 67035, 86009, 109541, 137923, 177493, 222027, 277749
OFFSET
0,8
FORMULA
G.f.: Sum_{k>=0} k! * x^(k*(k + 5)/2) / Product_{j=1..k} (1 - x^j).
EXAMPLE
a(7) = 3 because we have [7], [4, 3] and [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-> b(n$2, 0):
seq(a(n), n=0..50); # Alois P. Heinz, Nov 23 2020
MATHEMATICA
nmax = 50; CoefficientList[Series[Sum[k! x^(k (k + 5)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 23 2020
STATUS
approved