|
%I #15 Apr 30 2023 08:00:41
%S 1,1,6,132,11352,3882384,5303336544,28966824203328,632809241545903488,
%T 55296137144764138588416,19327437631660830304254690816,
%U 27021729207700270170039091739231232,151116480551518237100547636877027177224192
%N a(1) = 1, a(n) = Sum_{k=1..n-1} ((4^k - 1)/3)*a(k).
%H G. C. Greubel, <a href="/A015503/b015503.txt">Table of n, a(n) for n = 1..50</a>
%F a(n) = ((4^(n-1) + 2)/3) * a(n-1). - _Vincenzo Librandi_, Nov 11 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,4], {n,30}] (* _G. C. Greubel_, Apr 29 2023 *)
%o (Magma) [n le 2 select 1 else ((4^(n-1)+2)/3)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 11 2012
%o (SageMath)
%o @CachedFunction # a = A015503
%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,4) 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), this sequence (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).
%K nonn,easy
%O 1,3
%A _Olivier Gérard_
|
