A110378
a(n) = Sum_{prime p <= n} n!/p!.
Original entry on oeis.org
1, 4, 16, 81, 486, 3403, 27224, 245016, 2450160, 26951761, 323421132, 4204474717, 58862646038, 882939690570, 14127035049120, 240159595835041, 4322872725030738, 82134581775584023, 1642691635511680460
Offset: 2
a(6) = 6!(2! + 1/3! + 1/5!) = 486.
-
a:=proc(n) local s, i: s:=0: for i from 2 to n do if isprime(i)=true then s:=s+1/i! else s:=s: fi: od: n!*s: end: seq(a(n),n=2..23); # Emeric Deutsch, Jul 24 2005
A066045
Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = exp(((1-t)*(1-t^2)*(1-t^3)...)^(-u)-1).
Original entry on oeis.org
1, 3, 2, 8, 18, 5, 42, 118, 90, 15, 144, 900, 1075, 450, 52, 1440, 6788, 12375, 8475, 2340, 203, 5760, 61824, 141470, 140175, 63700, 12789, 877, 75600, 586584, 1700580, 2218335, 1441440, 474614, 73668, 4140, 524160, 6064416, 21677980
Offset: 1
Triangle begins:
[1],
[3, 2],
[8, 18, 5],
[42, 118, 90, 15],
[144, 900, 1075, 450, 52],
...
A110379
a(n) = Sum_{composite c <= n} n!/c!.
Original entry on oeis.org
1, 5, 31, 217, 1737, 15634, 156341, 1719751, 20637013, 268281169, 3755936367, 56339045506, 901424728097, 15324220377649, 275835966797683, 5240883369155977, 104817667383119541, 2201171015045510362
Offset: 4
a(6) = 6!(1/4! + 1/6!) = 31.
-
a:=proc(n) local s,i :s:=0: for i from 4 to n do if isprime(i)=false then s:=s+1/i! else s:=s: fi od: n!*s; end; seq(a(n),n=4..24); # Emeric Deutsch, Jul 25 2005