A258325 -id:A258325 - cp's OEIS frontend

A217757 Product_{i=0..n} (i! + 1).

2, 4, 12, 84, 2100, 254100, 183206100, 923541950100, 37238134969982100, 13513011656042074430100, 49036030210457135734021310100, 1957361459740805606124917565020990100, 937579272951542930363610919638075856505150100

Offset: 0

Jon Perry, Mar 23 2013

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..42

Cf. A000142, A000178, A054640, A082480, A258325, A260231, A306729.

function factorial(n) {
var i,c=1;
for (i=2;i<=n;i++) c*=i;
return c;
}
a=2;
for (j=1;j<10;j++) {
a*=(factorial(j)+1);
document.write(a+", ");
}

a:= proc(n) a(n):= `if`(n=0, 2, a(n-1)*(n!+1)) end:
seq(a(n), n=0..14);  # Alois P. Heinz, May 20 2013

Table[Product[i!+1,{i,0,n}],{n,0,12}]  (* Geoffrey Critzer, May 04 2013 *)
Rest[FoldList[Times,1,Range[0,15]!+1]] (* Harvey P. Dale, May 28 2013 *)

a(n) ~ c * A000178(n), where c = A238695 = Product_{k>=0} (1 + 1/k!) = 7.364308272367257256372772509631... . - Vaclav Kotesovec, Jul 20 2015

A260231 a(n) = Product_{k=1..n} (1 + k^k).

Original entry on oeis.org

2, 10, 280, 71960, 224946960, 10495350312720, 8643382777938679680, 145011908479540041684850560, 56180584638978557924165229531974400, 561805846445966163880630853243909229531974400, 160289764609087349005207761687490741791453382934816332800

Offset: 1

Vaclav Kotesovec, Jul 20 2015

nonn

Cf. A000312, A002109, A028361, A054640, A082480, A217757, A258325.

Table[Product[1+k^k,{k,1,n}],{n,1,12}]
FoldList[Times,Table[1+k^k,{k,12}]] (* Harvey P. Dale, Jul 19 2025 *)

a(n) ~ c * A002109(n), where c = Product_{k>=1} (1 + 1/k^k) = 2.60361190459951423330221282635022049352582879064202503882732200701325334...

cp's OEIS Frontend

A217757 Product_{i=0..n} (i! + 1).

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