The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A205566 G.f.: A(x) = 1 + x*A(x)*A(-x) + x^2*exp( Sum_{n>=1} 2*L(n)^2*x^(2*n)/n ), where A(x) = exp(Sum_{n>=1} L(n)*x^n/n). 1
 1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 17, 27, 44, 63, 71, 97, 98, 114, 203, 288, 498, 773, 3138, 5863, 8018, 10406, 19726, 32753, 40372, 47679, 89898, 154289, 199094, 277526, 439695, 742508, 880786, 1099183, 1765472, 2706524, 3378956, 4461436, 9651388, 16828143, 24527676 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Note: A(x)*A(-x) = exp( Sum_{n>=1} L(2*n)*x^(2*n)/n ) is a bisection of the g.f. A(x), where L(n) is the n-th coefficient in the logarithmic derivative of A(x). LINKS Paul D. Hanna, Table of n, a(n) for n = 0..512 EXAMPLE G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 3*x^6 + 3*x^7 + 4*x^8 +... Related expansions: A(x)*A(-x) = 1 + x^2 + 3*x^4 + 3*x^6 + 6*x^8 + 27*x^10 + 63*x^12 + 97*x^14 + 114*x^16 + 288*x^18 + 773*x^20 + 5863*x^22 + 10406*x^24 +... exp(Sum_{n>=1} 2*L(n)^2*x^(2*n)/n) = 1 + 2*x^2 + 3*x^4 + 4*x^6 + 17*x^8 + 44*x^10 + 71*x^12 + 98*x^14 + 203*x^16 + 498*x^18 + 3138*x^20 + 8018*x^22 +... log(A(x)) = x + x^2/2 + x^3/3 + 5*x^4/4 + 6*x^5/5 + x^6/6 + x^7/7 + 5*x^8/8 + 10*x^9/9 + 106*x^10/10 + 111*x^11/11 +...+ L(n)*x^n/n +... PROG (PARI) {a(n)=local(L=vector(n+1, i, 1), A=Ser(L)); for(i=1, n, A=1+x*A*subst(A, x, -x+x*O(x^n))+x^2*exp(2*sum(m=1, #L\2, x^(2*m)*L[m]^2/m)+x*O(x^n)); L=Vec(deriv(log(A)))); polcoeff(A, n)} CROSSREFS Sequence in context: A327718 A035581 A171628 * A064338 A197592 A103359 Adjacent sequences: A205563 A205564 A205565 * A205567 A205568 A205569 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 28 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 01:42 EDT 2024. Contains 372807 sequences. (Running on oeis4.)