A015502 a(1) = 1, a(n) = Sum_{k=1..n-1} (3^k - 1)/2 * a(k).

1, 1, 5, 70, 2870, 350140, 127801100, 139814403400, 458731057555400, 4514831068460246800, 133300387296288786770000, 11806948504381482999365980000, 3137354163532752044074527571580000, 2500979519710095684958538548015855960000

Offset

1,3

Links

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

Formula

a(n) = ((3^(n-1) + 1)/2) * a(n-1). - Vincenzo Librandi, Nov 11 2012

a(n) ~ c * 3^(n*(n-1)/2) / 2^(n+1), where c = A132323 = QPochhammer(-1, 1/3) = 3.129868... . - Vaclav Kotesovec, Mar 24 2017

Mathematica

Flatten[{1, Table[QPochhammer[-1, 3, n]/2^(n+1), {n, 2, 15}]}] (* Vaclav Kotesovec, Mar 24 2017 *)
a[n_, m_]:= a[n, m]= If[n<3, 1, (m^(n-1)+m-2)*a[n-1, m]/(m-1)];
Table[a[n, 3], {n, 20}] (* G. C. Greubel, Apr 29 2023 *)

Prog

(Magma) [n le 2 select 1 else ((3^(n-1)+1)/2)*Self(n-1): n in [1..15]]; // Vincenzo Librandi, Nov 11 2012
(SageMath)
@CachedFunction # a = A015502
def a(n, m): return 1 if (n<3) else (m^(n-1) + m-2)*a(n-1, m)/(m-1)
[a(n, 3) for n in range(1, 31)] # G. C. Greubel, Apr 29 2023

Crossrefs

Sequences with the recurrence a(n) = (m^(n-1) + m-2)*a(n-1)/(m-1): A036442 (m=2), this sequence (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), A015515 (m=12).

Cf. A156296.

Sequence in context: A370576 A174486 A135438 * A303291 A324229 A338989

Adjacent sequences: A015499 A015500 A015501 * A015503 A015504 A015505

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved