OFFSET
0,3
COMMENTS
Hankel transform is 7^C(n+1,2).
Series reversion of x*(1+x)*(1+2*x+8*x^2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} A120730(n,k) * 7^(n-k).
From G. C. Greubel, Nov 08 2022: (Start)
a(n) = 4*( 2*(n+1)*a(n-1) + 7*(n-2)*a(n-2) - 56*(n-2)*a(n-3) )/(n+1).
G.f.: (1 - sqrt(1 - 28*x^2))/(14*x^2 - x*(1 - sqrt(1 - 28*x^2))). (End)
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-28*x^2])/(14*x^2 -x*(1-Sqrt[1-28*x^2])), {x, 0, 40}], x] (* G. C. Greubel, Nov 08 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-28*x^2))/(14*x^2 -x*(1-Sqrt(1-28*x^2))) )); // G. C. Greubel, Nov 08 2022
(SageMath)
def A120730(n, k): return 0 if (n>2*k) else binomial(n, k)*(2*k-n+1)/(k+1)
[A132374(n) for n in range(51)] # G. C. Greubel, Nov 08 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Nov 10 2007
STATUS
approved