A015513 - OEIS

%I #13 May 04 2023 08:57:21

%S 1,1,13,1742,2552030,41102995180,7281683317103260,

%T 14189947350338830620680,304174136317707285574697584520,

%U 71722670512982436329410134761448960400,186030135925835196854820049614502274473787544400

%N a(1) = 1, a(n) = Sum_{k=1..n-1} ((11^k - 1)/10)*a(k).

%H G. C. Greubel, <a href="/A015513/b015513.txt">Table of n, a(n) for n = 1..45</a>

%F a(n) = ((11^(n-1) + 9)/10) * 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, 10], {n, 30}] (* _G. C. Greubel_, May 03 2023 *)

%o (Magma) [n le 2 select 1 else ((11^(n-1) + 9)/10) * Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 12 2012

%o (SageMath)

%o def a(n, m) -> int: # a = A015513

%o     return 1 if (n<3) else (m^(n-1)+m-2)*a(n-1, m)//(m-1)

%o [a(n, 11) 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), A015511 (m=9), A015512 (m=10), this sequence (m=11), A015515 (m=12).

%K nonn,easy

%O 1,3

%A _Olivier Gérard_