A015513 a(1) = 1, a(n) = Sum_{k=1..n-1} ((11^k - 1)/10)*a(k).

1, 1, 13, 1742, 2552030, 41102995180, 7281683317103260, 14189947350338830620680, 304174136317707285574697584520, 71722670512982436329410134761448960400, 186030135925835196854820049614502274473787544400

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..45

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), A015511 (m=9), A015512 (m=10), this sequence (m=11), A015515 (m=12).

Programs

Magma

[n le 2 select 1 else ((11^(n-1) + 9)/10) * 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, 10], {n, 30}] (* G. C. Greubel, May 03 2023 *)

SageMath

def a(n, m) -> int: # a = A015513
    return 1 if (n<3) else (m^(n-1)+m-2)*a(n-1, m)//(m-1)
[a(n, 11) for n in range(1,31)] # G. C. Greubel, May 03 2023

Formula

a(n) = ((11^(n-1) + 9)/10) * a(n-1). - Vincenzo Librandi, Nov 12 2012