login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339164 Number of compositions (ordered partitions) of n into distinct parts, the least being 3. 8
0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 50, 50, 80, 104, 134, 158, 212, 356, 410, 578, 752, 1040, 1238, 1646, 1964, 3236, 3674, 5066, 6368, 8720, 10862, 14078, 17180, 22076, 31802, 38378, 49784, 63824, 82670, 104150, 136220, 165980 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
FORMULA
G.f.: Sum_{k>=1} k! * x^(k*(k + 5)/2) / Product_{j=1..k-1} (1 - x^j).
EXAMPLE
a(12) = 8 because we have [9, 3], [5, 4, 3], [5, 3, 4], [4, 5, 3], [4, 3, 5], [3, 9], [3, 5, 4] and [3, 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-> `if`(n<3, 0, b(n-3$2, 1)):
seq(a(n), n=0..55); # Alois P. Heinz, Nov 25 2020
MATHEMATICA
nmax = 49; CoefficientList[Series[Sum[k! x^(k (k + 5)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A214080 A278241 A010671 * A323443 A334511 A291944
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 25 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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