cp's OEIS Frontend

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).

%I A163658 #2 Mar 30 2012 18:37:18
%S A163658 1,1,5,6,26,30,95,115,347,412,1076,1308,3277,3941,9081,11050,24694,
%T A163658 29834,63067,76711,158127,191360,379032,460448,893441,1081113,2035189,
%U A163658 2468182,4565994,5520070,9970503,12068315,21475803,25926236,45246532
%N 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).
%e A163658 G.f.: A(x) = 1 + x + 5*x^2 + 6*x^3 + 26*x^4 + 30*x^5 + 95*x^6 +...
%e A163658 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 +...
%e A163658 log(S(x)/x) = x + 3*x^2/2 - 2*x^3/3 + 7*x^4/4 + x^5/5 - 6*x^6/6 +...
%e A163658 where S(x) is the g.f. of Stern's diatomic series (A002487):
%e A163658 S(x) = x + x^2 + 2*x^3 + x^4 + 3*x^5 + 2*x^6 + 3*x^7 + x^8 + 4*x^9 +...
%o A163658 (PARI) {A002487(n)=local(c=1, b=0); while(n>0, if(bitand(n, 1), b+=c, c+=b); n>>=1); b}
%o A163658 {A163659(n)=n*polcoeff(log(sum(k=0,n,A002487(k+1)*x^k)+x*O(x^n)),n)}
%o A163658 {a(n)=polcoeff(exp(sum(k=1, n, A163659(k)^2*x^k/k)+x*O(x^n)), n)}
%Y A163658 Cf. A163659, A002487, A156302 (variant).
%K A163658 nonn
%O A163658 0,3
%A A163658 _Paul D. Hanna_, Aug 02 2009