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%I #23 Jan 23 2024 00:10:27
%S 1,1,1,1,2,3,4,5,6,8,11,15,20,26,33,41,51,64,81,103,131,166,209,261,
%T 323,397,486,594,726,888,1087,1331,1629,1991,2428,2952,3577,4320,5202,
%U 6249,7493,8973,10736,12838,15345,18334,21894,26127,31149,37092,44107,52368
%N Number of compositions of n where the smallest part is greater than or equal to the number of parts.
%H Vaclav Kotesovec, <a href="/A098131/b098131.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Sum_{k>=0} x^(k^2)/(1-x)^k.
%e a(7)=5 because we have 7, 4+3, 3+4, 5+2 and 2+5.
%p 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_
%t 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 *)
%o (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
%Y Cf. A003114, A077229.
%K easy,nonn
%O 0,5
%A _Vladeta Jovovic_, Sep 27 2004
%E More terms from _Emeric Deutsch_, Mar 29 2005
%E Prepended a(0)=1 to match g.f., _Joerg Arndt_, Apr 22 2014
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