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%I #16 May 03 2023 09:55:23
%S 1,1,11,1012,830852,6133349464,407444538242984,243599680968409330048,
%T 1310771150941736627904810368,63477451180042308935531134194562816,
%U 27666523379269090447091129488519658150671616
%N a(1) = 1, a(n) = Sum_{k=1..n-1} ((9^k - 1)/8)*a(k).
%H G. C. Greubel, <a href="/A015511/b015511.txt">Table of n, a(n) for n = 1..47</a>
%F a(n) = ((9^(n-1) + 7)/8) * a(n-1). - _Vincenzo Librandi_, Nov 12 2012
%F a(n) ~ QPochhammer(-63, 1/9) * 3^(n*(n-1)) / 2^(3*n+7). - _Vaclav Kotesovec_, May 03 2023
%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,9], {n,30}] (* _G. C. Greubel_, May 03 2023 *)
%t Join[{1}, Table[7^n*QPochhammer[-1/7, 9, n]/2^(3*n + 1), {n, 2, 12}]] (* _Vaclav Kotesovec_, May 03 2023 *)
%o (Magma) [n le 2 select 1 else ((9^(n-1)+7)/8)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 12 2012
%o (SageMath)
%o @CachedFunction # a = A015511
%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,9) for n in range(1, 31)] # _G. C. Greubel_, May 03 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), A015507 (m=6), A015508 (m=7), A015509 (m=8), this sequence (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).
%K nonn,easy
%O 1,3
%A _Olivier Gérard_
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