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A339104
Number of compositions (ordered partitions) of n into distinct parts >= 6.
7
1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 17, 17, 25, 31, 39, 45, 59, 65, 79, 115, 129, 165, 209, 269, 313, 403, 471, 585, 683, 941, 1063, 1375, 1641, 2097, 2537, 3161, 3745, 4663, 5535, 6741, 8627, 10241, 12535, 15307, 18849, 22869, 28409
OFFSET
0,14
FORMULA
G.f.: Sum_{k>=0} k! * x^(k*(k + 11)/2) / Product_{j=1..k} (1 - x^j).
EXAMPLE
a(13) = 3 because we have [13], [7, 6] and [6, 7].
MAPLE
b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-5)*(i+6)/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 = 57; CoefficientList[Series[Sum[k! x^(k (k + 11)/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