A131680 - OEIS

%I #26 Sep 08 2022 08:45:31

%S 1,11,54266008005,94467113468457039310,538562285352301951109430061,

%T 102370328298891480707678565453456,

%U 2171004564341130364494477279762016705,10015112821822553484101305268477882115400,15057116321451208557735379863635553426467625,9594364176429126945241161642390324911313805168

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

%C 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

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

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

%o (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

%o (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

%K nonn,easy

%O 0,2

%A _Alexander R. Povolotsky_, Sep 15 2007

%E Definition made explicit by _M. F. Hasler_, May 02 2015