OFFSET
0,2
COMMENTS
The sequence starting with a(1) is the binomial transform of A005563 starting with A005563(1). - Paul Curtz, Jan 02 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
E.g.f.: exp(x)*cosh(x) + exp(2*x)*(2*x+x^2/2); a(n) = 0^n/2 + 2^n*(n^2 + 7*n + 4)/8.
a(n) = Sum_{k=0..n-1} a(k) + (n+2)*2^(n-1) - 1. - Philippe Deléham, Jul 12 2007
G.f.: (-4 + 13*x - 16*x^2 + 8*x^3)/(2*x-1)^3. - R. J. Mathar, Jan 06 2011
a(n) = (Sum_{k=0..n+1} binomial(n+1,k)*k^4)/((n+1)*(n+2)), n > 0. - Gary Detlefs, Nov 26 2011
MATHEMATICA
LinearRecurrence[{6, -12, 8}, {1, 3, 11, 34}, 30] (* Harvey P. Dale, Dec 12 2021 *)
PROG
(Magma) [0^n/2+2^n*(n^2+7*n+4)/8: n in [0..35]]; // Vincenzo Librandi, Aug 13 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 31 2003
STATUS
approved