login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143918 G.f. A(x) satisfies: A(x) = 1/(1-x)^2 + x^2*A'(x). 1

%I

%S 1,2,5,14,47,194,977,5870,41099,328802,2959229,29592302,325515335,

%T 3906184034,50780392457,710925494414,10663882416227,170622118659650,

%U 2900576017214069,52210368309853262,991996997887211999,19839939957744240002,416638739112629040065

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

%H Alois P. Heinz, <a href="/A143918/b143918.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) = 3*floor(e*(n-1)!) - 1, n>1. - _Gary Detlefs_, Jun 10 2010

%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 14*x^3 + 47*x^4 + 194*x^5 + 977*x^6 +...

%e x^2*A'(x) = 2*x^2 + 10*x^3 + 42*x^4 + 188*x^5 + 970*x^6 + 5862*x^7 +...

%p a:= proc(n) option remember; `if`(n<3, n^2+1,

%p ((n^2+1)*a(n-1)-(n-2)*(n+1)*a(n-2))/n)

%p end:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 16 2017

%t a=2;lst={};Do[a=n+a*(n-2);AppendTo[lst,a],{n,0,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 16 2010 *)

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 05 2008

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 10 13:04 EDT 2020. Contains 335576 sequences. (Running on oeis4.)