A144071 Euler transform of powers of 7.

1, 7, 77, 770, 7609, 73178, 691971, 6438797, 59131499, 536802112, 4824305213, 42970458839, 379692684987, 3330902681785, 29030038318212, 251498296181846, 2166886679835829, 18575273870841254, 158486917413708492, 1346334588169264925, 11390431451798171304

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)^(7^j).

a(n) ~ 7^n * exp(2*sqrt(n) - 1/2 + c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} 1/(m*(7^(m-1)-1)) = 0.0911034105381918017167778099460538483167631... . - Vaclav Kotesovec, Mar 14 2015

G.f.: exp(7*Sum_{k>=1} x^k/(k*(1 - 7*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->7^j)(n): seq(a(n), n=0..40);

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1-x^j)^(7^j), {j, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)

Crossrefs

7th column of A144074.

Cf. A000420 (powers of 7).

Sequence in context: A043042 A191465 A229281 * A366596 A061546 A002281

Adjacent sequences: A144068 A144069 A144070 * A144072 A144073 A144074

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2008

Status

approved