A185954 G.f.: A(x) = exp( Sum_{n>=1} A163659(2n)*x^n/n ), where x*exp(Sum_{n>=1} A163659(n)*x^n/n) = S(x) is the g.f. of Stern's diatomic series (A002487).

1, 3, 8, 13, 23, 32, 49, 59, 80, 93, 127, 144, 185, 203, 256, 269, 319, 328, 401, 419, 504, 525, 639, 656, 761, 763, 904, 917, 1063, 1064, 1241, 1227, 1368, 1317, 1503, 1480, 1681, 1659, 1928, 1909, 2143, 2080, 2393, 2371, 2696, 2653, 3055, 2992, 3305, 3147

Offset: 0

Author

Paul D. Hanna, Feb 07 2011

Keywords

• nonn

Comments

Compare with g.f. of A171238: exp( Sum_{n>=1} A163659(3n)*x^n/n ).

Examples

			G.f.: A(x) = 1 + 3*x + 8*x^2 + 13*x^3 + 23*x^4 + 32*x^5 + 49*x^6 +...
log(A(x)) = 3*x + 7*x^2/2 - 6*x^3/3 + 15*x^4/4 + 3*x^5/5 - 14*x^6/6 + 3*x^7/7 + 31*x^8/8 - 6*x^9/9 +...+ A163659(2n)*x^n/n +...
		

Crossrefs

Cf. A163658, A163659, A171238, A002487.

Programs

PARI

{A002487(n)=local(c=1, b=0); while(n>0, if(bitand(n, 1), b+=c, c+=b); n>>=1); b}
{A163659(n)=n*polcoeff(log(sum(k=0, n, A002487(k+1)*x^k)+x*O(x^n)), n)}
{a(n)=polcoeff(exp(sum(k=1, n, A163659(2*k)*x^k/k)+x*O(x^n)), n)}

Formula

G.f. satisfies: A(x) = A(x^2)*(1+x)*(1-x^3)^2/[(1-x)^2*(1+x^3)].