A015515 a(1) = 1, a(n) = Sum_{k=1..n-1} ((12^k - 1)/11)*a(k).

1, 1, 14, 2212, 4171832, 94375183504, 25618521062894816, 83450744014073963641408, 3262026661649164626974053098368, 1530121919008888925087797696409496422656, 8612828743790947623482719127044813092555596516864

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..44

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), A015513 (m=11), this sequence (m=12).

Programs

Magma

[n le 2 select 1 else ((12^(n-1) + 10)/11) * Self(n-1): n in [1..15]]; // Vincenzo Librandi, Nov 12 2012

Mathematica

Join[{1},RecurrenceTable[{a[2]==1,a[n]==(12^(n-1)+10)/11 a[n-1]},a,{n,12}]] (* Harvey P. Dale, Mar 10 2013 *)

SageMath

def a(n, m) -> int: # a = A015515
    return 1 if (n<3) else (m^(n-1)+m-2)*a(n-1, m)//(m-1)
[a(n, 12) for n in range(1,31)] # G. C. Greubel, May 03 2023

Formula

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