A097976 Sum of largest parts (counted with multiplicity) in all compositions of n.

1, 4, 10, 24, 53, 118, 253, 542, 1143, 2396, 4986, 10330, 21304, 43808, 89837, 183838, 375514, 765880, 1559979, 3173794, 6450514, 13098246, 26574968, 53877266, 109153818, 221002456, 447199458, 904420716, 1828192748, 3693782678

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Formula

G.f.: (1-x)^2*Sum_{k>=1} k*x^k/(1 - 2*x + x^(k+1))^2.

Example

a(3)=10 because in the compositions 111, 12, 21, 3 the largest parts are 1, 2, 2, 3 with multiplicities 3, 1, 1, 1, respectively and 3*1 + 1*2 + 1*2 + 1*3 = 10.

Maple

G:=(1-x)^2*sum(k*x^k/(1-2*x+x^(k+1))^2, k=1..45): Gser:=series(G, x=0, 40): seq(coeff(Gser, x^n), n=1..35); # Emeric Deutsch, Jul 28 2005

Crossrefs

Cf. A097940, A092321.

Sequence in context: A080615 A173729 A340569 * A279851 A266367 A316528

Adjacent sequences: A097973 A097974 A097975 * A097977 A097978 A097979

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 07 2004

Extensions

More terms from Emeric Deutsch, Jul 28 2005

Status

approved