OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from Clark Kimberling)
FORMULA
a(n) = Sum_{k=1..n} n!/(n(1)!*n(2)!* ... *n(k)!), where n(i) = floor((n + i - 1)/k) for i = 1..k.
a(n) ~ 2 * n!. - Vaclav Kotesovec, Oct 21 2014
a(n) mod 2 = 0 <=> n in { A126646 } \ { 1 }. - Alois P. Heinz, Feb 20 2024
EXAMPLE
First seven rows of the array at A248686:
1
1 2
1 3 6
1 6 12 24
1 10 30 60 120
1 20 90 180 360 720
1 35 210 630 1260 2520 5040
The row sums are 1, 3, 10, ...
MAPLE
b:= proc(n, k) option remember; `if`(k<1,
`if`(n=k, 1, 0), n!/mul(iquo(n+i, k)!, i=0..k-1))
end:
a:= n-> add(b(n, k), k=0..n):
seq(a(n), n=1..22); # Alois P. Heinz, Feb 20 2024
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 11 2014
STATUS
approved