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A248687
Sum of the numbers in row n of the triangular array at A248686.
4
1, 3, 10, 43, 221, 1371, 9696, 78751, 712447, 7173853, 79106413, 952587175, 12397677007, 173864946685, 2609479384942, 41786786069887, 710577455524223, 12795789975272877, 243154034699436147, 4864103085730989101, 102153340062463300261, 2247608818115460466681
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
f[n_, k_] := f[n, k] = n!/Product[Floor[(n + i)/k]!, {i, 0, k - 1}]
t = Table[f[n, k], {n, 0, 10}, {k, 1, n}];
u = Flatten[t] (* A248686 sequence *)
TableForm[t] (* A248686 array *)
Table[Sum[f[n, k], {k, 1, n}], {n, 1, 22}] (* A248687 *)
CROSSREFS
Cf. A248686.
Sequence in context: A318372 A157313 A030971 * A006932 A001040 A181949
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 11 2014
STATUS
approved