OFFSET
1,2
COMMENTS
E.g.f. is g.f. for A001019(n-1) (powers of nine).
LINKS
FORMULA
9*a(n) = (9*n)(!^9) = Product_{j=1..n} 9*j = 9^n*n!.
E.g.f.: (-1+1/(1-9*x))/9.
D-finite with recurrence: a(n) - 9*n*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
From Amiram Eldar, Jan 08 2022: (Start)
Sum_{n>=1} 1/a(n) = 9*(exp(1/9)-1).
Sum_{n>=1} (-1)^(n+1)/a(n) = 9*(1-exp(-1/9)). (End)
From G. C. Greubel, Oct 19 2022: (Start)
MATHEMATICA
With[{nn=20}, Rest[CoefficientList[Series[(-1+1/(1-9*x))/9, {x, 0, nn}], x] Range[ 0, nn]!]] (* Harvey P. Dale, Apr 07 2019 *)
Table[9^(n-1)*n!, {n, 40}] (* G. C. Greubel, Oct 19 2022 *)
PROG
(Magma) [9^(n-1)*Factorial(n): n in [1..40]]; // G. C. Greubel, Oct 19 2022
(SageMath) [9^(n-1)*factorial(n) for n in range(1, 40)] # G. C. Greubel, Oct 19 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved