A131527 a(n) = 4*(n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)*(n^4 + 4!)*(n^5 + 5!)/5!.

1152, 4235, 51072, 1844766, 67267200, 1489787937, 20516082048, 194830108540, 1389727430784, 7923082634775, 37759956198272, 155476758621786, 566979054415488, 1866434208254637, 5629739963760000, 15745829707255032, 41231732634193024, 101887952581305891

Offset: 0

Author

Alexander R. Povolotsky, Aug 25 2007

Keywords

• nonn
• easy

Comments

Comment from Peter J. C. Moses, Aug 29 2007: the values of m = m(k) needed to make the sequence a(n,k) = m (n^1 + 1!) (n^2 + 2!) ... (n^i + k!) / k! (n >= 0) take integral values for all n are given in A049614.

Links

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

Programs

Mathematica

Table[(Times@@Table[n^k+k!,{k,5}])/30,{n,0,20}] (* Harvey P. Dale, Oct 12 2020 *)
LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{1152,4235,51072,1844766,67267200,1489787937,20516082048,194830108540,1389727430784,7923082634775,37759956198272,155476758621786,566979054415488,1866434208254637,5629739963760000,15745829707255032},30] (* Harvey P. Dale, May 15 2022 *)

Formula

G.f.: -(1408*x^14 -221419*x^13 -23074512*x^12 -437328710*x^11 -3130260112*x^10 -9871683909*x^9 -14838023712*x^8 -10832842836*x^7 -3802147872*x^6 -608960101*x^5 -43604624*x^4 -890694*x^3 -121552*x^2 +14197*x -1152) / (x -1)^16. - Colin Barker, Aug 08 2013