OFFSET
0,2
COMMENTS
Partial sums of A032020.
MAPLE
T:= proc(n, k) option remember; `if`(k<0 or n<0, 0,
`if`(k=0, `if`(n=0, 1, 0), T(n-k, k) +k*T(n-k, k-1)))
end:
b:= n-> add(T(n, k), k=0..floor((sqrt(8*n+1)-1)/2)):
a:= proc(n) option remember;
`if`(n<0, 0, b(n)+a(n-1))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Apr 28 2018
MATHEMATICA
nmax = 45; CoefficientList[Series[1/(1 - x) Sum[k! x^(k (k + 1)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 28 2018
STATUS
approved