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A098132 Number of compositions of n where the smallest part is greater than the number of parts. 2
0, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 27, 34, 42, 51, 62, 76, 94, 117, 146, 182, 226, 279, 342, 416, 503, 606, 729, 877, 1056, 1273, 1536, 1854, 2237, 2696, 3243, 3891, 4655, 5553, 6607, 7844, 9297, 11006, 13019, 15393, 18195, 21503, 25407, 30010 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: Sum_{n>=0} x^(n*(n+1)) / (1-x)^n.

EXAMPLE

a(11)=7 because we have: 11, 8+3, 3+8, 7+4, 4+7, 6+5 and 5+6.

MAPLE

G:=sum(x^(k^2+k)/(1-x)^k, k=0..20): Gser:=series(G, x=0, 67): seq(coeff(Gser, x^n), n=1..65); # Emeric Deutsch

MATHEMATICA

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

CROSSREFS

Cf. A003106, A003114, A077229.

Sequence in context: A042952 A126327 A193286 * A017900 A005708 A322853

Adjacent sequences:  A098129 A098130 A098131 * A098133 A098134 A098135

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 27 2004

EXTENSIONS

More terms from Emeric Deutsch, Mar 29 2005

STATUS

approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)