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a(1) = 1, a(n) = Sum_{k=1..n-1} ((6^k - 1)/5)*a(k).
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%I #17 Apr 30 2023 02:07:36

%S 1,1,8,352,91520,142405120,1328924579840,74403829376081920,

%T 24994031979330942894080,50376471215620688640734003200,

%U 609214555257707874214915513922355200,44204249911340791820804231319883906967142400

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

%H G. C. Greubel, <a href="/A015507/b015507.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) = ((6^(n-1) + 4)/5) * a(n-1). - _Vincenzo Librandi_, Nov 12 2012

%t a[n_,m_]:= a[n,m]= If[n<3, 1, (m^(n-1)+m-2)*a[n-1,m]/(m-1)];

%t Table[a[n,6], {n,20}] (* _G. C. Greubel_, Apr 29 2023 *)

%o (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 (SageMath)

%o @CachedFunction

%o def A015507(n): return 1 if (n<3) else (6^(n-1)+4)*A015507(n-1)/5

%o [A015507(n) for n in range(1,21)] # _G. C. Greubel_, Apr 29 2023

%Y 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 nonn,easy

%O 1,3

%A _Olivier GĂ©rard_