login
a(n) = n * (100^n - 1)/99.
1

%I #25 Nov 07 2024 09:53:39

%S 1,202,30303,4040404,505050505,60606060606,7070707070707,

%T 808080808080808,90909090909090909,10101010101010101010,

%U 1111111111111111111111,121212121212121212121212,13131313131313131313131313,1414141414141414141414141414,151515151515151515151515151515

%N a(n) = n * (100^n - 1)/99.

%C Recreational, but striking.

%H Harry J. Smith, <a href="/A064100/b064100.txt">Table of n, a(n) for n = 1..100</a>

%F From _G. C. Greubel_, Nov 07 2024: (Start)

%F a(n) = n*A094028(n-1).

%F G.f.: x*(1 - 100*x^2)/((1 - x)^2*(1 - 100*x)^2).

%F E.g.f.: (1/99)*x*(100*exp(100*x) - exp(x)). (End)

%t Table[(100^n-1)/99 n,{n,20}] (* _Harvey P. Dale_, Jul 25 2019 *)

%o (PARI) for(n=1, 22, print(n*(100^n-1)/99))

%o (Magma) [n*(100^n -1)/99: n in [1..20]]; // _G. C. Greubel_, Nov 07 2024

%o (SageMath) [n*(100^n -1)//99 for n in range(1,21)] # _G. C. Greubel_, Nov 07 2024

%Y Cf. A094028.

%K easy,nonn,changed

%O 1,2

%A _Jason Earls_, Sep 16 2001