A144070 Euler transform of powers of 6.

1, 6, 57, 488, 4140, 34128, 276792, 2208312, 17389710, 135354340, 1042965042, 7964675400, 60337114778, 453795079932, 3390657365970, 25182770127240, 186007882964211, 1366948744701066, 9998341947058175, 72811720605519840, 528078809473488744, 3815340122599096360

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

G.f.: Product_{j>0} 1/(1-x^j)^(6^j).

a(n) ~ 6^n * exp(2*sqrt(n) - 1/2 + c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} 1/(m*(6^(m-1)-1)) = 0.1108660629759785875628164141261367036457657... . - Vaclav Kotesovec, Mar 14 2015

G.f.: exp(6*Sum_{k>=1} x^k/(k*(1 - 6*x^k))). - Ilya Gutkovskiy, Nov 10 2018

Maple

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; `if`(n=0, 1, add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n) end end: a:=n-> etr(j->6^j)(n): seq(a(n), n=0..40);

Mathematica

etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b]; a[n_] := etr[Function[6^#]][n]; Table[ a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)

Crossrefs

6th column of A144074.

Cf. A000400 (powers of 6).

Sequence in context: A296027 A229280 A124546 * A095900 A161434 A332620

Adjacent sequences: A144067 A144068 A144069 * A144071 A144072 A144073

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2008

Status

approved