A107461 Number of gap-free compositions of n into distinct parts, cf. A107428.

1, 1, 3, 1, 3, 7, 3, 1, 9, 25, 3, 7, 3, 25, 129, 1, 3, 31, 3, 121, 729, 25, 3, 7, 123, 25, 729, 5041, 3, 151, 3, 1, 729, 25, 5163, 40327, 3, 25, 729, 121, 3, 5071, 3, 40321, 363729, 25, 3, 7, 5043, 145, 729, 40321, 3, 362911, 3628923, 5041, 729, 25, 3, 40447, 3, 25

Offset: 1

Author

Vladeta Jovovic, May 26 2005

Keywords

• easy
• nonn
• look

Examples

			a(6) = 7 because we have 6, 123, 132, 213, 231, 312 and 321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Programs

Maple

G:=sum(k!*x^(k*(k+1)/2)/(1-x^k),k=1..20): Gser:=series(G,x=0,73): seq(coeff(Gser,x^n),n=1..70); # Emeric Deutsch

Mathematica

nn=62;Drop[CoefficientList[Series[Sum[k!x^(k (k+1)/2)/(1-x^k),{k,1,nn}],{x,0,nn}],x],1] (* Geoffrey Critzer, Apr 13 2014 *)

PARI

N=66;  q='q+O('q^N);  S=1+2*sqrtint(N);
gf=sum(n=1,S, n! * q^(n*(n+1)/2) / (1-q^n) );
Vec(gf)
/* Joerg Arndt, Oct 20 2012 */

Formula

G.f.: Sum_{k>0} k!*x^(k*(k+1)/2)/(1-x^k).

Extensions

More terms from Emeric Deutsch, Jun 19 2005