OFFSET
0,2
COMMENTS
Partial sums are A162479.
LINKS
Robert Israel, Table of n, a(n) for n = 0..1163
FORMULA
G.f.: 1/(1-2x/((1-x)^4-x/(1-x/((1-x)^4-x/(1-... (continued fraction);
a(n) = Sum_{k=0..n} C(n+3k-1,n-k)*A000984(k).
D-finite with recurrence: n*a(n) +(7-9n)*a(n-1) +2*(7n-17)*a(n-2) +10*(3-n)*a(n-3) +5*(n-4)*a(n-4) +(5-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011
Recurrence confirmed using the differential equation (6*x+2)*g+(x^5-5*x^4+10*x^3-14*x^2+9*x-1)*g'=0 satisfied by the G.f. - Robert Israel, Dec 27 2017
a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (n+k) * binomial(n+2-k,3) * a(k). - Seiichi Manyama, Mar 28 2023
MAPLE
f:= gfun:-rectoproc({n*a(n) +(7-9*n)*a(n-1) +2*(7*n-17)*a(n-2) +10*(3-n)*a(n-3) +5*(n-4)*a(n-4) +(5-n)*a(n-5), a(0)=1, a(1)=2, a(2)=14, a(3)=88, a(4)=566}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Dec 27 2017
MATHEMATICA
CoefficientList[Series[1/Sqrt[1-(4x)/(1-x)^4], {x, 0, 20}], x] (* Harvey P. Dale, Aug 02 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 04 2009
STATUS
approved