The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A185618 G.f.: A(x) = 1/(1 - x/((1-x) - x/((1-x)^2 - x/((1-x)^3 -...)))), a continued fraction. 1

%I #7 Aug 26 2017 07:40:17

%S 1,1,3,12,57,306,1807,11538,78739,569533,4339187,34654038,288981540,

%T 2508261208,22599555849,210891194677,2034166628300,20245403842599,

%U 207589233294167,2189866971393096,23736645165616944,264066371438676327

%N G.f.: A(x) = 1/(1 - x/((1-x) - x/((1-x)^2 - x/((1-x)^3 -...)))), a continued fraction.

%H Vaclav Kotesovec, <a href="/A185618/b185618.txt">Table of n, a(n) for n = 0..300</a>

%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 57*x^4 + 306*x^5 + 1807*x^6 +...

%e Related functions.

%e Let A(x) = 1/(1 - x*B(x)), B(x) = 1/((1-x) - x*C(x)),

%e C(x) = 1/((1-x)^2 - x*D(x)), D(x) = 1/((1-x)^3 - x*E(x)),

%e E(x) = 1/((1-x)^4 - x*F(x)), F(x) = 1/((1-x)^5 - x*G(x)),

%e G(x) = 1/((1-x)^6 - x*H(x)), H(x) = 1/((1-x)^7 - x*I(x)), ...

%e then the coefficients in these functions begin:

%e B: [1,2,7,32,172,1035,6785,47667,355031,2782507,...];

%e C: [1,3,12,63,385,2604,19009,147520,1205168,10294340,...];

%e D: [1,4,18,106,726,5458,43987,374704,3342770,31032313,...];

%e E: [1,5,25,162,1226,10127,89216,827354,8005125,80319277,...];

%e F: [1,6,33,232,1917,17227,164430,1647071,17166202,185045995,...];

%e G: [1,7,42,317,2832,27461,281849,3028595,33790412,389155832,...];

%e H: [1,8,52,418,4005,41620,456429,5230214,62129311,760630876,...];

%e I: [1,9,63,536,5471,60584,706113,8584910,108063440,1400175142,...]; ...

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 05 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 4 10:24 EDT 2023. Contains 363121 sequences. (Running on oeis4.)