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

Author

Paul D. Hanna, Aug 02 2009

Keywords

• nonn

Examples

			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 +...
		

Crossrefs

Cf. A163659, A002487, A156302 (variant).

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