A098125 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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