OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).
FORMULA
a(n) = 2^(n-4)*(n^4+6*n^3+19*n^2+22*n+16). E.g.f.: (1+3*x+x^2)^2*exp(2*x). O.g.f.: (1-2*x+10*x^2-12*x^3+8*x^4)/(1-2*x)^5. Recurrence: a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5). a(n) = Sum_{k=0..n} binomial(n, k)*(k+1)^2*(n-k+1)^2. - Vladeta Jovovic, Sep 17 2003
MATHEMATICA
LinearRecurrence[{10, -40, 80, -80, 32}, {1, 8, 50, 248, 1048}, 30] (* Harvey P. Dale, Aug 26 2014 *)
CoefficientList[Series[(1 - 2 x + 10 x^2 - 12 x^3 + 8 x^4)/(1 - 2 x)^5, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 27 2014 *)
PROG
(Magma) I:=[1, 8, 50, 248, 1048]; [n le 5 select I[n] else 10*Self(n-1)-40*Self(n-2)+80*Self(n-3)-80*Self(n-4)+32*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Aug 27 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Aug 27 2014
STATUS
approved