OFFSET
0,3
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..449
FORMULA
a(n) = A096161(n) for n >= 1. - R. J. Mathar, Jun 26 2009
a(n) ~ n! * (1 + 1/n^2 + 2/n^3 + 7/n^4 + 28/n^5 + 121/n^6 + 587/n^7 + 3205/n^8 + 19201/n^9 + 123684/n^10), for coefficients see A293266. - Vaclav Kotesovec, Oct 04 2017
EXAMPLE
Let the partial products = a, a*b, a*b*c,..., with the first few rows =
(1, 1, 2, 6, 24, 120,...) = a
(1, 1, 3, 7, 28, 128,...) = a*b
(1, 1, 3, 8, 29, 131,...) = a*b*c
(1, 1, 3, 8, 30, 132,...) = a*b*c*d
...converging to A161779
MAPLE
read("transforms3") ; read("transforms") ; A161779 := proc(N) local a000142, res, n, j ; a000142 := [seq(n!, n=0..N)] ; res := [seq(op(n, a000142), n=1..N)] ; for j from 1 to N do res := CONV( res, AERATE(a000142, j)) ; od: [seq(op(n, res), n=1..N)] end: A161779(30) ; # R. J. Mathar, Jun 23 2009
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0 or i=1, n!,
add(b(n-i*j, i-1)*j!, j=0..n/i))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 03 2018, revised, Mar 05 2024
MATHEMATICA
b[n_, i_] := b[n, i] = If[i>n, 0, If[Mod[n, i] == 0, (n/i)!, 0] + Sum[j! b[n - i j, i + 1], {j, 0, n/i}]];
a[n_] := If[n == 0, 1, b[n, 1]];
a /@ Range[0, 25] (* Jean-François Alcover, Feb 04 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jun 19 2009
EXTENSIONS
Extended by R. J. Mathar, Jun 23 2009
STATUS
approved