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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A209766 A356207 A114972 * A035619 A280995 A092689

Adjacent sequences: A107458 A107459 A107460 * A107462 A107463 A107464

Keyword

easy,nonn,look

Author

Vladeta Jovovic, May 26 2005

Extensions

More terms from Emeric Deutsch, Jun 19 2005

Status

approved