A015509 a(1) = 1, a(n) = Sum_{k=1..n-1} ((8^k - 1)/7)*a(k).

1, 1, 10, 740, 433640, 2030302480, 76034827876000, 22779578222682344000, 54596862986901017252624000, 1046838176230046602563156976288000, 160576277008444677145920980328106246720000

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..48

Crossrefs

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).

Programs

Magma

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

Mathematica

a[n_, m_]:= a[n, m]= If[n<3, 1, (m^(n-1) +m-2)*a[n-1,m]/(m-1)];
Table[a[n,8], {n,30}] (* G. C. Greubel, Apr 30 2023 *)

SageMath

@CachedFunction # a = A015509
def a(n,m): return 1 if (n<3) else (m^(n-1)+m-2)*a(n-1,m)/(m-1)
[a(n,8) for n in range(1,31)] # G. C. Greubel, Apr 30 2023

Formula

a(n) = ((8^(n-1) + 6)/7) * a(n-1). - Vincenzo Librandi, Nov 12 2012