OFFSET
0,2
COMMENTS
The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(4*(m+1)*x)/3!.
LINKS
Index entries for linear recurrences with constant coefficients, signature (40, -560, 3200, -6144).
FORMULA
a(n) = (-4^n + 24*8^n - 81*12^n + 64*16^n)/3!.
G.f.: 1/Product_{k=1..4} (1 - 4*k*x).
E.g.f.: (d^4/dx^4)(((exp(4*x)-1)/4)^4)/4! = (-exp(4*x) + 24*exp(8*x) - 81*exp(12*x) + 64*exp(16*x))/3!.
a(0)=1, a(1)=40, a(2)=1040, a(3)=22400, a(n) = 40*a(n-1) - 560*a(n-2) + 3200*a(n-3) - 6144*a(n-4). - Harvey P. Dale, Jun 04 2013
MATHEMATICA
Table[(-4^n+24*8^n-81*12^n+64*16^n)/6, {n, 0, 20}] (* or *) LinearRecurrence[ {40, -560, 3200, -6144}, {1, 40, 1040, 22400}, 20] (* Harvey P. Dale, Jun 04 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 02 2002
STATUS
approved