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!)
 A295536 G.f. A(x) satisfies: A(x) = 1 + x*A(x)^6 - x^2/A(x)^26. 1

%I #7 Jan 13 2018 04:41:26

%S 1,1,5,71,375,6682,44580,946312,6922752,145981865,1096808573,

%T 24010330078,187616411332,4183857848749,33458964526535,

%U 752695079265278,6129198925216730,139043863694798233,1150329560451062383,26226063866647040405,219806629752765285995,5027613613859350046965,42619409376237650116405,976900179567084519322460,8365478066582587330962470

%N G.f. A(x) satisfies: A(x) = 1 + x*A(x)^6 - x^2/A(x)^26.

%C Note that G(x) such that G(x) = 1 + x*G(x)^6 - x^2/G(x)^27 has negative coefficients.

%H Paul D. Hanna, <a href="/A295536/b295536.txt">Table of n, a(n) for n = 0..500</a>

%F G.f. A(x) satisfies: x^2 = A(x)^26 - A(x)^27 + x*A(x)^32.

%e G.f. A(x) = 1 + x + 5*x^2 + 71*x^3 + 375*x^4 + 6682*x^5 + 44580*x^6 + 946312*x^7 + 6922752*x^8 + 145981865*x^9 + 1096808573*x^10 + 24010330078*x^11 + 187616411332*x^12 + 4183857848749*x^13 + 33458964526535*x^14 + 752695079265278*x^15 +...

%e such that A(x) = 1 + x*A(x)^6 - x^2/A(x)^26.

%e RELATED SERIES.

%e A(x)^6 = 1 + 6*x + 45*x^2 + 596*x^3 + 5070*x^4 + 68058*x^5 + 674066*x^6 + 9948762*x^7 + 106491843*x^8 + 1599019100*x^9 +...

%e 1/A(x)^26 = 1 - 26*x + 221*x^2 - 1612*x^3 + 23478*x^4 - 272246*x^5 + 3026010*x^6 - 39490022*x^7 + 502210527*x^8 +...

%e A(x)^26 = 1 + 26*x + 455*x^2 + 7696*x^3 + 117975*x^4 + 1761812*x^5 + 25510485*x^6 + 368086862*x^7 + 5245565832*x^8 +...

%e A(x)^27 = 1 + 27*x + 486*x^2 + 8352*x^3 + 130167*x^4 + 1967004*x^5 + 28797525*x^6 + 418814334*x^7 + 6013769832*x^8 +...

%e A(x)^32 = 1 + 32*x + 656*x^2 + 12192*x^3 + 205192*x^4 + 3287040*x^5 + 50727472*x^6 + 768204000*x^7 + 11445866084*x^8 +...

%e where x^2 = A(x)^26 - A(x)^27 + x*A(x)^32.

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1 + x*A^6 - x^2/A^26 +x*O(x^n)); polcoeff(G=A, n)}

%o for(n=0, 40, print1(a(n), ", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 23 2017

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 25 12:29 EDT 2024. Contains 372788 sequences. (Running on oeis4.)