A131680 a(n) = (Product_{i=1..10} n^i+i)/10!.

1, 11, 54266008005, 94467113468457039310, 538562285352301951109430061, 102370328298891480707678565453456, 2171004564341130364494477279762016705, 10015112821822553484101305268477882115400, 15057116321451208557735379863635553426467625, 9594364176429126945241161642390324911313805168

Offset: 0

Author

Alexander R. Povolotsky, Sep 15 2007

Keywords

• nonn
• easy

Comments

See also A131685(k) = smallest positive number m such that c(i) = m (i^1 + 1) (i^2 + 2) ... (i^k+ k) / k! takes integral values for all i>=0: For k=10, A131685(k)=1, which implies that this is a well defined integer sequence. - Alexander R. Povolotsky, Apr 24 2015; corrected by M. F. Hasler, May 02 2015

Links

• Index to divisibility sequences

Programs

Magma

[((n+1)*(n^2+2)*(n^3+3)*(n^4+4)*(n^5+5)*(n^6+6)*(n^7+7)*(n^8+8)*(n^9+9)*(n^10+10))/Factorial(10): n in [0..10]]; // Vincenzo Librandi, Apr 25 2015

Mathematica

Table[x = 10; Product[(n^k) + k, {k, x}]/x!, {n, 0, 9}] (* Michael De Vlieger, Apr 24 2015 *)

PARI

A131680(n,k=10)=prod(i=1,k,(n^i+i))/k! \\ Changing the optional 2nd argument allows one to produce A000027 (k=1), A064808 (k=2), A131509 (k=3), A129995 (k=4), A131675(k=5), ..., A131679 (k=9). - M. F. Hasler, May 02 2015

Extensions

Definition made explicit by M. F. Hasler, May 02 2015