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%I #13 Apr 30 2023 02:06:17
%S 1,1,7,224,35168,27501376,107447876032,2098671914657024,
%T 204950003169660992768,100073397447688408870744576,
%U 244319893042568615235897903058432,2982420752607212448380293251367177293824
%N a(1) = 1, a(n) = Sum_{k=1}^{n-1} (5^k - 1)/4 a(k).
%H G. C. Greubel, <a href="/A015506/b015506.txt">Table of n, a(n) for n = 1..50</a>
%F a(n) = ((5^(n-1) + 3)/4) * 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, 5], {n, 20}] (* _G. C. Greubel_, Apr 29 2023 *)
%o (Magma) [n le 2 select 1 else ((5^(n-1)+3)/4)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 12 2012
%o (SageMath)
%o @CachedFunction # a = A015506
%o def a(n,m): return 1 if (n<3) else (m^(n-1) + m-2)*a(n-1,m)/(m-1)
%o [a(n,5) for n in range(1,31)] # _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), this sequence (m=5), A015507 (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 Gérard_
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