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!)
 A191803 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(5*n^2). 5

%I #4 Mar 30 2012 18:37:26

%S 1,1,6,61,791,11701,188462,3225915,57840755,1076423857,20666351126,

%T 407645638428,8237858879315,170229866493435,3592746391559133,

%U 77393340642273491,1701286171473636404,38169860244429063080

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(5*n^2).

%F Let A = g.f. A(x), then A satisfies:

%F (1) A = Sum_{n>=0} x^n*A^(5*n)*Product_{k=1..n} (1-x*A^(20*k-15))/(1-x*A^(20*k-5));

%F (2) A = 1/(1- A^5*x/(1- A^5*(A^10-1)*x/(1- A^25*x/(1- A^15*(A^20-1)*x/(1- A^45*x/(1- A^25*(A^30-1)*x/(1- A^65*x/(1- A^35*(A^40-1)*x/(1- ...))))))))) (continued fraction);

%F due to a q-series identity and an identity of a partial elliptic theta function, respectively.

%e G.f.: A(x) = 1 + x + 6*x^2 + 61*x^3 + 791*x^4 + 11701*x^5 + 188462*x^6 +...

%e where the g.f. satisfies:

%e A(x) = 1 + x*A(x)^5 + x^2*A(x)^20 + x^3*A(x)^45 + x^4*A(x)^80 +...+ x^n*A(x)^(5*n^2) +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(5*m^2)));polcoeff(A,n)}

%Y Cf. A107595, A191800, A191801, A191802, A191804.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 16 2011

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 June 18 17:16 EDT 2024. Contains 373482 sequences. (Running on oeis4.)