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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 24 13:20 EDT 2024. Contains 372773 sequences. (Running on oeis4.)