A015507 a(1) = 1, a(n) = Sum_{k=1..n-1} ((6^k - 1)/5)*a(k).

1, 1, 8, 352, 91520, 142405120, 1328924579840, 74403829376081920, 24994031979330942894080, 50376471215620688640734003200, 609214555257707874214915513922355200, 44204249911340791820804231319883906967142400

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..50

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), this sequence (m=6), A015508 (m=7), A015509 (m=8), A015511 (m=9), A015512 (m=10), A015513 (m=11), A015515 (m=12).

Programs

Magma

[n le 2 select 1 else ((6^(n-1)+4)/5)*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,6], {n,20}] (* G. C. Greubel, Apr 29 2023 *)

SageMath

@CachedFunction
def A015507(n): return 1 if (n<3) else (6^(n-1)+4)*A015507(n-1)/5
[A015507(n) for n in range(1,21)] # G. C. Greubel, Apr 29 2023

Formula

a(n) = ((6^(n-1) + 4)/5) * a(n-1). - Vincenzo Librandi, Nov 12 2012