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A107461 Number of gap-free compositions of n into distinct parts, cf. A107428. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A208916 A209766 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

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Last modified July 23 14:44 EDT 2021. Contains 346259 sequences. (Running on oeis4.)