OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1-x-sqrt(1-6*x+x^2))/(2*x*sqrt(1-4*x)). - corrected by Georg Fischer, Apr 09 2020
a(n) = Sum_{k=0..n} C(2*k, k)*( Sum_{j=0..n-k} C(n-k+j, n-k)*C(n-k, j)/(j+1) ).
a(n) ~ sqrt(4 + sqrt(2)) * (1 + sqrt(2))^(2*n + 2) / (2*sqrt(7*Pi)*n^(3/2)). - Vaclav Kotesovec, Sep 14 2021
MATHEMATICA
CoefficientList[Series[(1-x-(Sqrt[1-6*x+x^2]))/(2x*Sqrt[1-4*x]), {x, 0, 30}] (* Georg Fischer, Apr 09 2020 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (1-x-Sqrt(1-6*x+x^2))/(2*x*Sqrt(1-4*x)) )); // G. C. Greubel, Sep 24 2021
(Sage)
def A110276_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x-sqrt(1-6*x+x^2))/(2*x*sqrt(1-4*x)) ).list()
A110276_list(30)
(PARI) a(n) = sum(k=0, n, binomial(2*k, k)*sum(j=0, n-k, binomial(n-k+j, n-k)*binomial(n-k, j)/(j+1))); \\ Michel Marcus, Sep 25 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 18 2005
STATUS
approved