A015515 - OEIS

%I #15 May 04 2023 08:57:17

%S 1,1,14,2212,4171832,94375183504,25618521062894816,

%T 83450744014073963641408,3262026661649164626974053098368,

%U 1530121919008888925087797696409496422656,8612828743790947623482719127044813092555596516864

%N a(1) = 1, a(n) = Sum_{k=1..n-1} ((12^k - 1)/11)*a(k).

%H G. C. Greubel, <a href="/A015515/b015515.txt">Table of n, a(n) for n = 1..44</a>

%F a(n) = ((12^(n-1) + 10)/11) * a(n-1). - _Vincenzo Librandi_, Nov 12 2012

%t Join[{1},RecurrenceTable[{a[2]==1,a[n]==(12^(n-1)+10)/11 a[n-1]},a,{n,12}]] (* _Harvey P. Dale_, Mar 10 2013 *)

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

%o (SageMath)

%o def a(n, m) -> int: # a = A015515

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

%o [a(n, 12) 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), A015513 (m=11), this sequence (m=12).

%K nonn,easy

%O 1,3

%A _Olivier Gérard_