OFFSET
0,2
COMMENTS
Diagonal sums of number triangle A128417.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k)*C(2n-2k,n-2k).
D-finite with recurrence: 3*n*(15*n-22)*a(n) = 4*(75*n^2-155*n+63)*a(n-1) + (465*n^2-922*n+336)*a(n-2) + 4*(2*n-3)*(15*n-7)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012
a(n) ~ 2^(3*n+4)/(15*sqrt(Pi*n)) . - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
CoefficientList[Series[8/(Sqrt[1-8x](Sqrt[1-8x]+4x+7)), {x, 0, 30}], x] (* Harvey P. Dale, Apr 24 2012 *)
Table[Sum[2^(n-2*k)*Binomial[2*n-2*k, n-2*k], {k, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, Feb 09 2017 *)
PROG
(PARI) x='x+O('x^50); Vec(8/(sqrt(1-8*x)*(sqrt(1-8*x)+4*x+7))) \\ G. C. Greubel, Feb 09 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 02 2007
STATUS
approved