A015511 a(1) = 1, a(n) = Sum_{k=1..n-1} ((9^k - 1)/8)*a(k).

1, 1, 11, 1012, 830852, 6133349464, 407444538242984, 243599680968409330048, 1310771150941736627904810368, 63477451180042308935531134194562816, 27666523379269090447091129488519658150671616

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..47

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

Programs

Magma

[n le 2 select 1 else ((9^(n-1)+7)/8)*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,9], {n,30}] (* G. C. Greubel, May 03 2023 *)
Join[{1}, Table[7^n*QPochhammer[-1/7, 9, n]/2^(3*n + 1), {n, 2, 12}]] (* Vaclav Kotesovec, May 03 2023 *)

SageMath

@CachedFunction # a = A015511
def a(n, m): return 1 if (n<3) else (m^(n-1)+m-2)*a(n-1, m)/(m-1)
[a(n,9) for n in range(1, 31)] # G. C. Greubel, May 03 2023

Formula

a(n) = ((9^(n-1) + 7)/8) * a(n-1). - Vincenzo Librandi, Nov 12 2012

a(n) ~ QPochhammer(-63, 1/9) * 3^(n*(n-1)) / 2^(3*n+7). - Vaclav Kotesovec, May 03 2023