A098124 Number of compositions of n in which the largest part is equal to the number of parts.

1, 0, 2, 1, 3, 6, 10, 15, 30, 54, 92, 160, 282, 492, 859, 1490, 2570, 4428, 7627, 13098, 22421, 38290, 65265, 111018, 188475, 319380, 540266, 912397, 1538371, 2589858, 4353820, 7309362, 12255474, 20523307, 34328731, 57357184, 95733131, 159626049

Offset

1,3

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

a(7)=10 because we have 223, 232, 322, 133, 313, 331, 1114, 1141, 1411 and 4111.

Maple

G:=sum(((x^(k+1)-x)^k-(x^k-x)^k)/(x-1)^k, k=1..25):Gser:=series(G, x=0, 45):seq(coeff(Gser, x^n), n=1..42); # Emeric Deutsch, Apr 16 2005

Crossrefs

Cf. A077229, A047993.

Sequence in context: A329101 A024866 A076058 * A020992 A025110 A075346

Adjacent sequences: A098121 A098122 A098123 * A098125 A098126 A098127

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 25 2004

Extensions

More terms from Emeric Deutsch, Apr 16 2005

Status

approved