cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A015512 a(1) = 1, a(n) = Sum_{k=1..n-1} ((10^k - 1)/9)*a(k).

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%I A015512 #13 May 03 2023 09:11:45
%S A015512 1,1,12,1344,1494528,16607195136,1845258665951232,
%T A015512 2050289046842405289984,22780991231839211526404702208,
%U A015512 2531221268231904597902043824359735296,2812468078063201791652852780757078172764209152
%N A015512 a(1) = 1, a(n) = Sum_{k=1..n-1} ((10^k - 1)/9)*a(k).
%H A015512 G. C. Greubel, <a href="/A015512/b015512.txt">Table of n, a(n) for n = 1..46</a>
%F A015512 a(n) = ((10^(n-1) + 8)/9) * a(n-1). - _Vincenzo Librandi_, Nov 12 2012
%t A015512 a[n_, m_]:= a[n, m]= If[n<3, 1, (m^(n-1) +m-2)*a[n-1,m]/(m-1)];
%t A015512 Table[a[n, 10], {n, 30}] (* _G. C. Greubel_, May 03 2023 *)
%o A015512 (Magma) [n le 2 select 1 else ((10^(n-1) + 8)/9)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 12 2012
%o A015512 (SageMath)
%o A015512 @CachedFunction # a = A015512
%o A015512 def a(n, m): return 1 if (n<3) else (m^(n-1)+m-2)*a(n-1, m)/(m-1)
%o A015512 [a(n,10) for n in range(1, 31)] # _G. C. Greubel_, May 03 2023
%Y A015512 Sequences with the recurrence a(n) = (m^(n-1) + m-2)*a(n-1)/(m-1): A036442 (m=2),  A015502 (m=3), A015503 (m=4), A015506 (m=5), A015507 (m=6), A015508 (m=7), A015509 (m=8), A015511 (m=9), this sequence (m=10), A015513 (m=11), A015515 (m=12).
%K A015512 nonn,easy
%O A015512 1,3
%A A015512 _Olivier Gérard_