OFFSET
0,2
LINKS
FORMULA
a(n) = 9*A035278(n) = (10*n-1)(!^10), n >= 1, a(0) = 1.
a(n) = (-1)^n*Sum_{k=0..n} 10^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
a(n) = 10^n * Gamma(n+9/10) / Gamma(9/10). - Vaclav Kotesovec, Jan 28 2015
E.g.f.: (1-10*x)^(-9/10). - Vaclav Kotesovec, Jan 28 2015
From Nikolaos Pantelidis, Jan 17 2021: (Start)
G.f.: 1/G(0) where G(k) = 1 - (20*k+9)*x - 10*(k+1)*(10*k+9)*x^2/G(k+1) (continued fraction).
G.f.: 1/(1-9*x-90*x^2/(1-29*x-380*x^2/(1-49*x-870*x^2/(1-69*x-1560*x^2/(1-89*x-2450*x^2/(1-...)))))) (Jacobi continued fraction).
G.f.: 1/Q(0) where Q(k) = 1 - x*(10*k+9)/(1 - x*(10*k+10)/Q(k+1)) (continued fraction).
G.f.: 1/(1-9*x/(1-10*x/(1-19*x/(1-20*x/(1-29*x/(1-30*x/(1-39*x/(1-40*x/(1-49*x/(1-50*x/(1-...))))))))))) (Stieltjes continued fraction).
(End)
G.f.: Hypergeometric2F0([1, 9/10], --; 10*x). - G. C. Greubel, Feb 03 2022
Sum_{n>=0} 1/a(n) = 1 + (e/10)^(1/10)*(Gamma(9/10) - Gamma(9/10, 1/10)). - Amiram Eldar, Dec 22 2022
MATHEMATICA
CoefficientList[Series[(1-10*x)^(-9/10), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2015 *)
PROG
(PARI) a(n) = {-prod(k=0, n, 10*k-1)} \\ Andrew Howroyd, Jan 02 2020
(Magma) [Round(10^n*Gamma(n+9/10)/Gamma(9/10)): n in [0..25]]; // G. C. Greubel, Feb 03 2022
(Sage) [10^n*rising_factorial(9/10, n) for n in (0..25)] # G. C. Greubel, Feb 03 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Jan 02 2020
STATUS
approved