A163658 G.f.: A(x) = exp( Sum_{n>=1} A163659(n)^2*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, 1, 5, 6, 26, 30, 95, 115, 347, 412, 1076, 1308, 3277, 3941, 9081, 11050, 24694, 29834, 63067, 76711, 158127, 191360, 379032, 460448, 893441, 1081113, 2035189, 2468182, 4565994, 5520070, 9970503, 12068315, 21475803, 25926236, 45246532

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Example

G.f.: A(x) = 1 + x + 5*x^2 + 6*x^3 + 26*x^4 + 30*x^5 + 95*x^6 +...
log(A(X)) = x + 3^2*x^2/2 + 2^2*x^3/3 + 7^2*x^4/4 + x^5/5 + 6^2*x^6/6 +...
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 +...

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(k)^2*x^k/k)+x*O(x^n)), n)}

Crossrefs

Cf. A163659, A002487, A156302 (variant).

Sequence in context: A088834 A137081 A137079 * A121180 A022165 A342775

Adjacent sequences: A163655 A163656 A163657 * A163659 A163660 A163661

Keyword

nonn

Author

Paul D. Hanna, Aug 02 2009

Status

approved