%I #13 May 01 2023 18:02:09

%S 1,1,10,740,433640,2030302480,76034827876000,22779578222682344000,

%T 54596862986901017252624000,1046838176230046602563156976288000,

%U 160576277008444677145920980328106246720000

%N a(1) = 1, a(n) = Sum_{k=1..n-1} ((8^k - 1)/7)*a(k).

%H G. C. Greubel, <a href="/A015509/b015509.txt">Table of n, a(n) for n = 1..48</a>

%F a(n) = ((8^(n-1) + 6)/7) * 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,8], {n,30}] (* _G. C. Greubel_, Apr 30 2023 *)

%o (Magma) [n le 2 select 1 else ((8^(n-1)+6)/7)*Self(n-1): n in [1..15]]; // _Vincenzo Librandi_, Nov 12 2012

%o (SageMath)

%o @CachedFunction # a = A015509

%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,8) for n in range(1,31)] # _G. C. Greubel_, Apr 30 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), this sequence (m=8), A015511 (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).

%K nonn,easy

%O 1,3

%A _Olivier Gérard_