A098125 Number of compositions of n where the largest part is less than the number of parts.

0, 1, 1, 4, 8, 17, 38, 83, 174, 367, 771, 1606, 3324, 6849, 14054, 28743, 58605, 119161, 241717, 489345, 988945, 1995604, 4021710, 8095815, 16281400, 32716231, 65694106, 131833462, 264423116, 530128036, 1062424867, 2128513095

Offset

1,4

Links

Table of n, a(n) for n=1..32.

Formula

G.f.: Sum_{k>=0} ((x^k-x)/(x-1))^k.

Example

a(5)=8 because we have 1112, 1121, 1211, 2111, 122, 212, 221 and 11111.

Maple

G:=sum(((x^k-x)/(x-1))^k, k=0..45): Gser:=series(G, x=0, 40): seq(coeff(Gser, x^n), n=1..36); # Emeric Deutsch, Apr 16 2005

Crossrefs

Cf. A077229, A047993, A064173, A064174.

Sequence in context: A115618 A019479 A084814 * A335274 A296399 A119471

Adjacent sequences: A098122 A098123 A098124 * A098126 A098127 A098128

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 25 2004

Extensions

More terms from Emeric Deutsch, Apr 16 2005

Status

approved