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A163659 L.g.f.: Sum_{n>=1} a(n)*x^n/n = log(S(x)/x) where S(x) is the g.f. of Stern's diatomic series (A002487). +0
2
1, 3, -2, 7, 1, -6, 1, 15, -2, 3, 1, -14, 1, 3, -2, 31, 1, -6, 1, 7, -2, 3, 1, -30, 1, 3, -2, 7, 1, -6, 1, 63, -2, 3, 1, -14, 1, 3, -2, 15, 1, -6, 1, 7, -2, 3, 1, -62, 1, 3, -2, 7, 1, -6, 1, 15, -2, 3, 1, -14, 1, 3, -2, 127, 1, -6, 1, 7, -2, 3, 1, -30, 1, 3, -2, 7, 1, -6, 1, 31, -2, 3, 1, -14, 1 (list; graph; listen)
OFFSET

1,2

FORMULA

a(2^n) = 2^(n+1) - 1 for n>=0.

EXAMPLE

L.g.f.: log(S(x)/x) = x + 3*x^2/2 - 2*x^3/3 + 7*x^4/4 + x^5/5 - 6*x^6/6 +...

where S(x) is the g.f. of Stern's diatomic series (A002487):

S(x) = x + x^2 + 2*x^3 + x^4 + 3*x^5 + 2*x^6 + 3*x^7 + x^8 + 4*x^9 +...

PROGRAM

(PARI) {A002487(n)=local(c=1, b=0); while(n>0, if(bitand(n, 1), b+=c, c+=b); n>>=1); b}

{a(n)=n*polcoeff(log(sum(k=0, n, A002487(k+1)*x^k)+x*O(x^n)), n)}

CROSSREFS

Cf. A163658, A002487.

Sequence in context: A019951 A019971 A010606 this_sequence A010760 A085594 A085587

Adjacent sequences: A163656 A163657 A163658 this_sequence A163660 A163661 A163662

KEYWORD

sign

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Aug 02 2009

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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