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A144071 Euler transform of powers of 7. 2
1, 7, 77, 770, 7609, 73178, 691971, 6438797, 59131499, 536802112, 4824305213, 42970458839, 379692684987, 3330902681785, 29030038318212, 251498296181846, 2166886679835829, 18575273870841254, 158486917413708492, 1346334588169264925, 11390431451798171304 (list; graph; refs; listen; history; text; internal format)
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 * A061546 A002281 A097983

Adjacent sequences:  A144068 A144069 A144070 * A144072 A144073 A144074

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 09 2008

STATUS

approved

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Last modified June 4 03:37 EDT 2020. Contains 334815 sequences. (Running on oeis4.)