OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = 2*A063886(n-1) + (n+1)*[n<2].
G.f.: 1 + 2*x*sqrt((1+2*x)/(1-2*x)). - Michael Somos
E.g.f.: 1 - x*BesselI(1, 2*x)*(2 + Pi*(1 + 2*x)*StruveL(0, 2*x)) + x*(1 + 2*x)*BesselI(0, 2*x)*(2 + Pi*StruveL(1, 2*x)). - Stefano Spezia, May 11 2024
MATHEMATICA
Table[If[n<2, n+1, 4*Binomial[n-2, Floor[(n-2)/2]]], {n, 0, 40}] (* G. C. Greubel, Oct 13 2022 *)
PROG
(PARI) a(n) = if(n<2, max(0, n+1), 4*binomial(n-2, n\2-1))
(Magma) [n le 1 select n+1 else 4*Binomial(n-2, Floor((n-2)/2)): n in [0..40]]; // G. C. Greubel, Oct 13 2022
(SageMath) [4*binomial(n-2, ((n-2)//2)) + (n+1)*int(n<2) for n in range(41)] # G. C. Greubel, Oct 13 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved