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A098131 Number of compositions of n where the smallest part is greater than or equal to the number of parts. 2
1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 11, 15, 20, 26, 33, 41, 51, 64, 81, 103, 131, 166, 209, 261, 323, 397, 486, 594, 726, 888, 1087, 1331, 1629, 1991, 2428, 2952, 3577, 4320, 5202, 6249, 7493, 8973, 10736, 12838, 15345, 18334, 21894, 26127, 31149, 37092, 44107, 52368 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: sum(k>=0, x^(k^2)/(1-x)^k ).

EXAMPLE

a(7)=5 because we have 7, 4+3, 3+4, 5+2 and 2+5.

MAPLE

G:=sum(x^(k^2)/(1-x)^k, k=0..20): Gser:=series(G, x=0, 56): seq( coeff( Gser, x^n), n=0..54);  # Emeric Deutsch

MATHEMATICA

nmax = 60; Flatten[{1, Rest[CoefficientList[Series[Sum[x^(k^2)/(1-x)^k, {k, 1, Sqrt[nmax]}], {x, 0, nmax}], x]]}] (* Vaclav Kotesovec, Nov 11 2018 *)

PROG

(PARI) N=66; q='q+O('q^N);

gf=sum(n=0, N, q^(n^2) / (1-q)^n );

v=Vec(gf) \\ Joerg Arndt, Mar 30 2014

CROSSREFS

Cf. A003114, A077229.

Sequence in context: A060967 A218930 A026483 * A017899 A003520 A101915

Adjacent sequences:  A098128 A098129 A098130 * A098132 A098133 A098134

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 27 2004

EXTENSIONS

More terms from Emeric Deutsch, Mar 29 2005

Prepended a(0)=1 to match g.f., Joerg Arndt, Apr 22 2014

STATUS

approved

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Last modified August 18 07:11 EDT 2019. Contains 326072 sequences. (Running on oeis4.)