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%I #19 Apr 13 2023 08:30:27
%S 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,
%T 226,279,342,416,503,606,729,877,1056,1273,1536,1854,2237,2696,3243,
%U 3891,4655,5553,6607,7844,9297,11006,13019,15393,18195,21503,25407,30010
%N Number of compositions of n where the smallest part is greater than the number of parts.
%H Vaclav Kotesovec, <a href="/A098132/b098132.txt">Table of n, a(n) for n = 1..10000</a>
%H Hung Viet Chu, Nurettin Irmak, Steven J. Miller, Laszlo Szalay, and Sindy Xin Zhang, <a href="https://arxiv.org/abs/2304.05409">Schreier Multisets and the s-step Fibonacci Sequences</a>, arXiv:2304.05409 [math.CO], 2023.
%F G.f.: Sum_{n>=0} x^(n*(n+1)) / (1-x)^n.
%e a(11)=7 because we have: 11, 8+3, 3+8, 7+4, 4+7, 6+5 and 5+6.
%p 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_, Mar 29 2005
%t 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 *)
%Y Cf. A003106, A003114, A077229.
%K easy,nonn
%O 1,6
%A _Vladeta Jovovic_, Sep 27 2004
%E More terms from _Emeric Deutsch_, Mar 29 2005
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