A131675 a(n) = (Product_{i=1..5} n^i+i)/5!.

1, 6, 1221, 231880, 13443885, 340203456, 4910472385, 47565216504, 342540938025, 1962871989130, 9382270310061, 38701449021984, 141297910237237, 465502930269300, 1404867737405385, 3930816255364816, 10296122969028753, 25448298063869070, 59744930256741205

Offset

0,2

Comments

See A131685 about well-definedness. - M. F. Hasler, May 02 2015

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

G.f.: (135*x^14 +86852*x^13 +5864611*x^12 +109724496*x^11 +782427151*x^10 +2468818430*x^9 +3704965659*x^8 +2710222344*x^7 +952834509*x^6 +152249688*x^5 +9878785*x^4 +212504*x^3 +1245*x^2 -10*x +1) / (x -1)^16. - Colin Barker, Apr 24 2015

Mathematica

Table[x = 5; Product[(n^k) + k, {k, x}]/x!, {n, 0, 17}] (* Michael De Vlieger, Apr 24 2015 *)
LinearRecurrence[{16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1}, {1, 6, 1221, 231880, 13443885, 340203456, 4910472385, 47565216504, 342540938025, 1962871989130, 9382270310061, 38701449021984, 141297910237237, 465502930269300, 1404867737405385, 3930816255364816}, 20] (* Harvey P. Dale, Oct 04 2024 *)

Prog

(PARI) Vec((135*x^14 +86852*x^13 +5864611*x^12 +109724496*x^11 +782427151*x^10 +2468818430*x^9 +3704965659*x^8 +2710222344*x^7 +952834509*x^6 +152249688*x^5 +9878785*x^4 +212504*x^3 +1245*x^2 -10*x +1) / (x -1)^16 + O(x^100)) \\ Colin Barker, Apr 24 2015
(Magma) [((n+1)*(n^2+2)*(n^3+3)*(n^4+4)*(n^5+5))/Factorial(5): n in [0..20]]; // Vincenzo Librandi, Apr 25 2015
(PARI) A131675(n, k=5)=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), A131676 (k=6), ..., A131680 (k=10). - M. F. Hasler, May 02 2015

Crossrefs

Sequence in context: A160857 A160005 A172923 * A263437 A001324 A183585

Adjacent sequences: A131672 A131673 A131674 * A131676 A131677 A131678

Keyword

nonn,easy

Author

Alexander R. Povolotsky, Sep 15 2007

Extensions

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

Status

approved