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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A195737 E.g.f.: x = Sum_{n>=1} a(n)*x^n/n! * exp(-n*(n+1)/2*x). 3

%I #14 Dec 03 2015 19:11:11

%S 1,2,15,256,7935,392526,28498246,2863702080,381411964485,

%T 65129544696250,13888321460879976,3620285828450155008,

%U 1133432920326577483795,419923892646668363653350,181795302703808044653240000,90971411268941227901619966976

%N E.g.f.: x = Sum_{n>=1} a(n)*x^n/n! * exp(-n*(n+1)/2*x).

%C Compare e.g.f. to: x = Sum_{n>=1} n^(n-1)*x^n/n! * exp(-n*x), which generates coefficients for the series reversion of x*exp(-x).

%H Alois P. Heinz, <a href="/A195737/b195737.txt">Table of n, a(n) for n = 1..200</a>

%F G.f.: x = Sum_{n>=1} a(n)*x^n/(n*(1 + n*(n+1)/2*x)^n).

%e x = x*exp(-x) + 2*x^2/2!*exp(-3*x) + 15*x^3/3!*exp(-6*x) + 256*x^4/4!*exp(-10*x) + 7935*x^5/5!*exp(-15*x) +...+ a(n)*x^n/n!*exp(-n*(n+1)/2*x) +...

%e The coefficients a(n) also satisfy:

%e x = x/(1+x) + 2*x^2/(2*(1+3*x)^2) + 15*x^3/(3*(1+6*x)^3) + 256*x^4/(4*(1+10*x)^4) + 7935*x^5/(5*(1+15*x)^5) +...+ a(n)*x^n/(n*(1+n*(n+1)/2*x)^n) +...

%o (PARI) {a(n)=if(n<1,0,n!*polcoeff(x-sum(m=1,n-1,a(m)*x^m/m!*exp(-m*(m+1)/2*x+x*O(x^n))),n))}

%o (PARI) {a(n)=if(n<1,0,n*polcoeff(x-sum(m=1,n-1,a(m)*x^m/(m*(1+m*(m+1)/2*x+x*O(x^n))^m)),n))}

%Y Cf. A195736, A196304.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Sep 30 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 September 8 06:37 EDT 2024. Contains 375751 sequences. (Running on oeis4.)