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A098125 Number of compositions of n where the largest part is less than the number of parts. 2
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

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

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Last modified January 17 20:06 EST 2022. Contains 350410 sequences. (Running on oeis4.)