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

1, 15, -2, 127, 1, -30, 1, 1023, -2, 15, 1, -254, 1, 15, -2, 8191, 1, -30, 1, 127, -2, 15, 1, -2046, 1, 15, -2, 127, 1, -30, 1, 65535, -2, 15, 1, -254, 1, 15, -2, 1023, 1, -30, 1, 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

Offset: 1

Author

Paul D. Hanna, May 03 2014

Keywords

• sign
• mult

Comments

Multiplicative because A163659 is. - Andrew Howroyd, Jul 27 2018

Examples

			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 +...
where
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 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A237646, A163659.

Programs

PARI

{A163659(n)=if(n<1, 0, if(n%3, 1, -2)*sigma(2^valuation(n, 2)))}
{a(n)=A163659(n^3)}
for(n=1,64,print1(a(n),", "))

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)}
for(n=1,64,print1(a(n),", "))

Formula

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.

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)).