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A097976 Sum of largest parts (counted with multiplicity) in all compositions of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A280541 A080615 A173729 * 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

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Last modified January 15 18:55 EST 2021. Contains 340188 sequences. (Running on oeis4.)