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 A156335 G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients. 2

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

%S 1,2,4,16,92,1816,47344,4888640,546663016,245429690704,

%T 113080892367776,209848258185362560,393950238751186551328,

%U 2976605303522286162203456,22642571073509592590956639360,692351532949951721637759480882688

%N G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

%F a(n) = (1/n)*Sum_{k=1..n} 2^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1.

%e G.f.: A(x) = 1 + 2*x + 4*x^2 + 16*x^3 + 92*x^4 + 1816*x^5 + 47344*x^6 +...

%e log(A(x)) = 2*x + 2^2*x^2/2 + 2^5*x^3/3 + 2^8*x^4/4 + 2^13*x^5/5 + 2^18*x^6/6 +...

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

%Y Cf. A156334, A156336, A156337, A155200.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 10 2009

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Last modified August 11 01:05 EDT 2024. Contains 375059 sequences. (Running on oeis4.)