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%I #20 Apr 30 2023 08:00:34
%S 1,1,5,70,2870,350140,127801100,139814403400,458731057555400,
%T 4514831068460246800,133300387296288786770000,
%U 11806948504381482999365980000,3137354163532752044074527571580000,2500979519710095684958538548015855960000
%N a(1) = 1, a(n) = Sum_{k=1..n-1} (3^k - 1)/2 * a(k).
%H G. C. Greubel, <a href="/A015502/b015502.txt">Table of n, a(n) for n = 1..50</a>
%F a(n) = ((3^(n-1) + 1)/2) * a(n-1). - _Vincenzo Librandi_, Nov 11 2012
%F a(n) ~ c * 3^(n*(n-1)/2) / 2^(n+1), where c = A132323 = QPochhammer(-1, 1/3) = 3.129868... . - _Vaclav Kotesovec_, Mar 24 2017
%t Flatten[{1, Table[QPochhammer[-1, 3, n]/2^(n+1), {n, 2, 15}]}] (* _Vaclav Kotesovec_, Mar 24 2017 *)
%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,3], {n,20}] (* _G. C. Greubel_, Apr 29 2023 *)
%o (Magma) [n le 2 select 1 else ((3^(n-1)+1)/2)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 11 2012
%o (SageMath)
%o @CachedFunction # a = A015502
%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,3) 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), this sequence (m=3), A015503 (m=4), A015506 (m=5), A015507 (m=6), A015508 (m=7), A015509 (m=8), A015511 (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).
%Y Cf. A156296.
%K nonn,easy
%O 1,3
%A _Olivier Gérard_
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