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.

A015507 a(1) = 1, a(n) = Sum_{k=1..n-1} ((6^k - 1)/5)*a(k).

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%I A015507 #17 Apr 30 2023 02:07:36
%S A015507 1,1,8,352,91520,142405120,1328924579840,74403829376081920,
%T A015507 24994031979330942894080,50376471215620688640734003200,
%U A015507 609214555257707874214915513922355200,44204249911340791820804231319883906967142400
%N A015507 a(1) = 1, a(n) = Sum_{k=1..n-1} ((6^k - 1)/5)*a(k).
%H A015507 G. C. Greubel, <a href="/A015507/b015507.txt">Table of n, a(n) for n = 1..50</a>
%F A015507 a(n) = ((6^(n-1) + 4)/5) * a(n-1). - _Vincenzo Librandi_, Nov 12 2012
%t A015507 a[n_,m_]:= a[n,m]= If[n<3, 1, (m^(n-1)+m-2)*a[n-1,m]/(m-1)];
%t A015507 Table[a[n,6], {n,20}] (* _G. C. Greubel_, Apr 29 2023 *)
%o A015507 (Magma) [n le 2 select 1 else ((6^(n-1)+4)/5)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 12 2012
%o A015507 (SageMath)
%o A015507 @CachedFunction
%o A015507 def A015507(n): return 1 if (n<3) else (6^(n-1)+4)*A015507(n-1)/5
%o A015507 [A015507(n) for n in range(1,21)] # _G. C. Greubel_, Apr 29 2023
%Y A015507 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), this sequence (m=6), A015508 (m=7), A015509 (m=8), A015511 (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).
%K A015507 nonn,easy
%O A015507 1,3
%A A015507 _Olivier Gérard_