A015506 a(1) = 1, a(n) = Sum_{k=1}^{n-1} (5^k - 1)/4 a(k).

1, 1, 7, 224, 35168, 27501376, 107447876032, 2098671914657024, 204950003169660992768, 100073397447688408870744576, 244319893042568615235897903058432, 2982420752607212448380293251367177293824

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), this sequence (m=5), A015507 (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 ((5^(n-1)+3)/4)*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, 5], {n, 20}] (* G. C. Greubel, Apr 29 2023 *)

SageMath

@CachedFunction # a = A015506
def a(n,m): return 1 if (n<3) else (m^(n-1) + m-2)*a(n-1,m)/(m-1)
[a(n,5) for n in range(1,31)] # G. C. Greubel, Apr 29 2023

Formula

a(n) = ((5^(n-1) + 3)/4) * a(n-1). - Vincenzo Librandi, Nov 12 2012