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 A155210 G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n/3^(n-1) * x^n/n ), a power series in x with integer coefficients. 4

%I

%S 1,3,42,9378,39179127,2766569881269,3234201150559172040,

%T 62076685218110095082936700,19446778350632942283719042004313725,

%U 98999235365955012033013202024947235500115415

%N G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n/3^(n-1) * x^n/n ), a power series in x with integer coefficients.

%C More generally, for m integer, exp( Sum_{n>=1} (m^n - 1)^n/(m-1)^(n-1) * x^n/n ) is a power series in x with integer coefficients.

%C Note that g.f. exp( Sum_{n>=1} (4^n - 1)^n/3^n * x^n/n ) has fractional coefficients as a power series in x.

%e G.f.: A(x) = 1 + 3*x + 42*x^2 + 9378*x^3 + 39179127*x^4 +...

%e log(A(x)) = 3*x + 15^2/3*x^2/2 + 63^3/3^2*x^3/3 + 255^4/3^3*x^4/4 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(4^m-1)^m/3^(m-1)*x^m/m)+x*O(x^n)),n)}

%Y Cf. A155207, A155208, A155209, variant: A155206.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2009

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Last modified February 25 23:44 EST 2020. Contains 332270 sequences. (Running on oeis4.)