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

0,2

Comments

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

Links

Table of n, a(n) for n=0..49.

Formula

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

Example

 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 +...

Prog

 (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)}

Crossrefs

Cf. A163658, A163659, A171238, A002487.

Sequence in context: A351355 A194427 A335048 * A051838 A076792 A146939

Adjacent sequences: A185951 A185952 A185953 * A185955 A185956 A185957

Keyword

nonn

Author

Paul D. Hanna, Feb 07 2011

Status

approved