%I #19 Nov 10 2018 05:47:17
%S 1,7,77,770,7609,73178,691971,6438797,59131499,536802112,4824305213,
%T 42970458839,379692684987,3330902681785,29030038318212,
%U 251498296181846,2166886679835829,18575273870841254,158486917413708492,1346334588169264925,11390431451798171304
%N Euler transform of powers of 7.
%H Alois P. Heinz, <a href="/A144071/b144071.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt"> Transforms</a>
%F G.f.: Product_{j>0} 1/(1-x^j)^(7^j).
%F 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
%F G.f.: exp(7*Sum_{k>=1} x^k/(k*(1 - 7*x^k))). - _Ilya Gutkovskiy_, Nov 10 2018
%p 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);
%t nmax = 20; CoefficientList[Series[Product[1/(1-x^j)^(7^j), {j, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 14 2015 *)
%Y 7th column of A144074.
%Y Cf. A000420 (powers of 7).
%K nonn
%O 0,2
%A _Alois P. Heinz_, Sep 09 2008
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