OFFSET
0,3
COMMENTS
Sum of all parts of all compositions (ordered partitions) of n into distinct parts.
FORMULA
a(n) = n*A032020(n).
MAPLE
b:= proc(n, k) option remember; `if`(k<0 or n<0, 0,
`if`(k=0, `if`(n=0, 1, 0), b(n-k, k) +k*b(n-k, k-1)))
end:
a:= n-> n*add(b(n, k), k=0..floor((sqrt(8*n+1)-1)/2)):
seq(a(n), n=0..50); # Alois P. Heinz, May 18 2018
MATHEMATICA
nmax = 39; CoefficientList[Series[x D[Sum[k! x^(k (k + 1)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], x], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 18 2018
STATUS
approved