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 A158110 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^3)*x^n/n ). 2

%I #2 Mar 30 2012 18:37:16

%S 1,2,130,44739500,4611686018516874838,

%T 8507059173023461595807737228465099196,

%U 17552048611426197782986337964292523732529439672780432120964458900

%N G.f.: A(x) = exp( Sum_{n>=1} 2^(n^3)*x^n/n ).

%C Conjecture: given q and m are nonnegative integers, then

%C exp( Sum_{n>=1} q^(n^m)*x^n/n )

%C is a power series in x with integer coefficients.

%e G.f.: A(x) = 1 + 2*x + 130*x^2 + 44739500*x^3 +...

%e log(A(x)) = 2*x + 2^8*x^2/2 + 2^27*x^3/3 + 2^64*x^4/4 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^3)*x^m/m)+x*O(x^n)), n)}

%Y Cf. A155200.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 19 2009

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Last modified April 16 07:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)