cp's OEIS Frontend

A237649 a(n) = A163659(n^3), where A163659 is the logarithmic derivative of Stern's diatomic series (A002487).

%I A237649 #12 Jul 27 2018 17:39:28
%S A237649 1,15,-2,127,1,-30,1,1023,-2,15,1,-254,1,15,-2,8191,1,-30,1,127,-2,15,
%T A237649 1,-2046,1,15,-2,127,1,-30,1,65535,-2,15,1,-254,1,15,-2,1023,1,-30,1,
%U A237649 127,-2,15,1,-16382,1,15,-2,127,1,-30,1,1023,-2,15,1,-254,1,15,-2,524287,1,-30,1,127
%N A237649 a(n) = A163659(n^3), where A163659 is the logarithmic derivative of Stern's diatomic series (A002487).
%C A237649 Multiplicative because A163659 is. - _Andrew Howroyd_, Jul 27 2018
%H A237649 Paul D. Hanna, <a href="/A237649/b237649.txt">Table of n, a(n) for n = 1..1000</a>
%F A237649 L.g.f.: log(1+x+x^2) + Sum_{n>=0} 7*4^n * log(1 + x^(2*2^n) + x^(4*2^n)) = Sum_{n>=1} a(n)*x^n/n.
%F A237649 G.f.: x*(1+2*x)/(1+x+x^2) + Sum_{n>=0} 14*8^n * x^(2*2^n) * (1 + 2*x^(2*2^n)) / (1 + x^(2*2^n) + x^(4*2^n)).
%e A237649 L.g.f.: L(x) = x + 15*x^2/2 - 2*x^3/3 + 127*x^4/4 + x^5/5 - 30*x^6/6 + x^7/7 + 1023*x^8/8 +...+ A163659(n^3)*x^n/n +...
%e A237649 where
%e A237649 exp(L(x)) = 1 + x + 8*x^2 + 7*x^3 + 63*x^4 + 56*x^5 + 329*x^6 + 273*x^7 + 1736*x^8 +...+ A237646(n)*x^n +...
%o A237649 (PARI) {A163659(n)=if(n<1, 0, if(n%3, 1, -2)*sigma(2^valuation(n, 2)))}
%o A237649 {a(n)=A163659(n^3)}
%o A237649 for(n=1,64,print1(a(n),", "))
%o A237649 (PARI) {a(n)=local(X=x+x*O(x^n),A);A=log(1+X+X^2) + sum(k=0,#binary(n),7*4^k*log(1 + X^(2*2^k) + X^(4*2^k)));n*polcoeff(A,n)}
%o A237649 for(n=1,64,print1(a(n),", "))
%Y A237649 Cf. A237646, A163659.
%K A237649 sign,mult
%O A237649 1,2
%A A237649 _Paul D. Hanna_, May 03 2014