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A098131
Number of compositions of n where the smallest part is greater than or equal to the number of parts.
3
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
OFFSET
0,5
LINKS
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) my(N=66, x='x+O('x^N)); Vec(sum(n=1, N, x^(n*n)*(1)/(1-x)^n)) \\ Joerg Arndt, Jan 23 2024
CROSSREFS
Sequence in context: A218930 A350391 A026483 * A017899 A003520 A101915
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