A131683 a(n) = 4*(n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)*(n^4 + 4!)/4!.

48, 175, 1680, 25410, 294000, 2295513, 12991440, 57550100, 211281840, 669529875, 1885734928, 4823347830, 11387316720, 25126129245, 52326450000, 103659864168, 196585724720, 358766207415, 632810010000, 1082730294250, 1802581066608, 2927824829985, 4650083620560

Offset: 0

Author

Alexander R. Povolotsky, Aug 29 2007

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

See A049614.

Programs

Mathematica

Table[((n+1)(n^2+2)(n^3+6)(n^4+24))/6,{n,0,30}] (* or *) LinearRecurrence[ {11,-55,165,-330,462,-462,330,-165,55,-11,1},{48,175,1680,25410,294000,2295513,12991440,57550100,211281840,669529875,1885734928},30] (* Harvey P. Dale, Mar 23 2015 *)

Formula

G.f.: -(80*x^9 +7205*x^8 +61625*x^7 +213873*x^6 +217437*x^5 +93855*x^4 +8635*x^3 +2395*x^2 -353*x +48) / (x -1)^11. - Colin Barker, Aug 08 2013

a(0)=48, a(1)=175, a(2)=1680, a(3)=25410, a(4)=294000, a(5)=2295513, a(6)=12991440, a(7)=57550100, a(8)=211281840, a(9)=669529875, a(10)=1885734928, a(n)=11*a(n-1)- 55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)- 165*a(n-8)+ 55*a(n-9)- 11*a(n-10)+a(n-11). - Harvey P. Dale, Mar 23 2015