A195737 E.g.f.: x = Sum_{n>=1} a(n)*x^n/n! * exp(-n*(n+1)/2*x).
1, 2, 15, 256, 7935, 392526, 28498246, 2863702080, 381411964485, 65129544696250, 13888321460879976, 3620285828450155008, 1133432920326577483795, 419923892646668363653350, 181795302703808044653240000, 90971411268941227901619966976
Offset: 1
Keywords
Examples
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) +... The coefficients a(n) also satisfy: 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) +...
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..200
Programs
-
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))} -
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))}
Formula
G.f.: x = Sum_{n>=1} a(n)*x^n/(n*(1 + n*(n+1)/2*x)^n).
Comments