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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085022 Integer floor of coefficients of exp(x*A(x)). 3

%I #14 Apr 29 2015 14:10:22

%S 1,1,1,2,4,8,17,37,82,185,424,983,2301,5431,12913,30900,74361,179855,

%T 436974,1065985,2609993,6411730,15799090,39039031,96711591,240150955,

%U 597640140,1490309462,3723343793,9318686066,23360994967,58654055246

%N Integer floor of coefficients of exp(x*A(x)).

%H Vaclav Kotesovec, <a href="/A085022/b085022.txt">Table of n, a(n) for n = 0..350</a>

%F a(n) = floor(A085023(n)/n!) where exp(x*A(x)) = sum(n>=0, A085023(n)*x^n/n!).

%F a(n) ~ c * d^n / n^(3/2), where d = 2.6325509689919889304486..., c = 0.99440959889640775375... . - _Vaclav Kotesovec_, Apr 27 2015

%e exp(x*(1 + x + floor(3/2!)*x^2 + floor(13/3!)*x^3 + floor(97/4!)*x^4 + ...)) = 1 + x + (3/2!)*x^2 + (13/3!)*x^3 + (97/4!)*x^4 + ...

%e 1 + x + floor(3/2)*x^2 + floor(13/6)*x^3 + floor(97/24)*x^4 + ... = 1 + x + x^2 + 2*x^3 + 4*x^4 + ...

%o (PARI) {a(n)=local(A); if(n<0,0,A=1+O(x); for(m=1,n,A=Pol(A)+x^m*(floor(polcoeff(exp(x*A),m))+O(x)); ); polcoeff(A,n))}

%Y Cf. A085023, A085294.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Jun 18 2003

%E Example added by _Vaclav Kotesovec_, Apr 27 2015

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)