OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..300
FORMULA
G.f.: 1/(1-11*x/(1-12*x/(1-23*x/(1-24*x/(1-35*x/(1-36*x/(1-47*x/(1-48*x/(1-59*x/(1-60*x/(1-...))))))))))) (Stieltjes continued fraction).
G.f.: 1/Q(0) where Q(k) = 1 - x*(12*k+11)/(1 - x*(12*k+12)/Q(k+1) ) (continued fraction).
G.f.: 1/(1-11*x-132*x^2/(1-35*x-552*x^2/(1-59*x-1260*x^2/(1-83*x-2256*x^2/(1-107*x-3540*x^2/(1-...)))))) (Jacobi continued fraction).
G.f.: 1/G(0) where G(k) = 1 - x*(24*k+11) - 12*(k+1)*(12*k+11)*x^2/G(k+1) (continued fraction).
a(n) = 12^n*Gamma(n+11/12)/Gamma(11/12). - Stefano Spezia, Aug 07 2021
Sum_{n>=0} 1/a(n) = 1 + (e/12)^(1/12)*(Gamma(11/12) - Gamma(11/12, 1/12)). - Amiram Eldar, Dec 22 2022
MATHEMATICA
CoefficientList[Series[(1-12*x)^(-11/12), {x, 0, 20}], x] * Range[0, 20]!
FullSimplify[Table[12^n Gamma[n+11/12]/Gamma[11/12], {n, 0, 15}]] (* Stefano Spezia, Aug 07 2021 *)
PROG
(Sage) m=12; [m^n*rising_factorial((m-1)/m, n) for n in (0..20)] # G. C. Greubel, Feb 16 2022
(Magma) m:=12; [Round(m^n*Gamma(n +(m-1)/m)/Gamma((m-1)/m)): n in [0..20]]; // G. C. Greubel, Feb 16 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Nikolaos Pantelidis, Aug 06 2021
STATUS
approved