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A339102
Number of compositions (ordered partitions) of n into distinct parts >= 4.
7
1, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 15, 15, 23, 29, 37, 43, 57, 87, 101, 137, 175, 235, 279, 363, 431, 665, 757, 1015, 1257, 1683, 2069, 2645, 3199, 4063, 5607, 6759, 8591, 10877, 13837, 17251, 22185, 26871, 33773, 41273, 56047, 66499, 85647, 104811
OFFSET
0,10
FORMULA
G.f.: Sum_{k>=0} k! * x^(k*(k + 7)/2) / Product_{j=1..k} (1 - x^j).
EXAMPLE
a(9) = 3 because we have [9], [5, 4] and [4, 5].
MAPLE
b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-3)*(i+4)/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..60); # Alois P. Heinz, Nov 23 2020
MATHEMATICA
nmax = 52; CoefficientList[Series[Sum[k! x^(k (k + 7)/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