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

1,2

Comments

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).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Formula

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

Example

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) +...

Prog

(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))}

Crossrefs

Cf. A195736, A196304.

Sequence in context: A203310 A102555 A264907 * A192567 A354980 A143886

Adjacent sequences: A195734 A195735 A195736 * A195738 A195739 A195740

Keyword

nonn

Author

Paul D. Hanna, Sep 30 2011

Status

approved