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A321481 Expansion of Sum_{n>=1} q^(n*(n-1)) / (1-q)^n.

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%I A321481 #10 May 13 2024 12:22:37
%S A321481 1,1,2,3,4,5,7,10,14,19,25,32,41,53,69,90,117,151,193,244,306,382,476,
%T A321481 593,739,921,1147,1426,1768,2184,2687,3293,4022,4899,5955,7228,8764,
%U A321481 10618,12855,15551,18794,22685,27340,32893,39500,47344,56641,67647,80666,96059,114254,135757,161164,191174,226603,268399
%N A321481 Expansion of Sum_{n>=1} q^(n*(n-1)) / (1-q)^n.
%H A321481 Vaclav Kotesovec, <a href="/A321481/b321481.txt">Table of n, a(n) for n = 0..10000</a>
%F A321481 G.f.: Sum_{n>=1} q^(n*(n-1)) / (1-q)^n.
%t A321481 nmax = 60; CoefficientList[Series[Sum[x^(k*(k-1))/(1-x)^k, {k, 1, Sqrt[nmax] + 1}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 11 2018 *)
%o A321481 (PARI) N=66; q='q+O('q^N); Vec( sum(n=1,N,q^(n*(n-1))/(1-q)^n) )
%Y A321481 Cf. A098132 (expansion of Sum_{n>=0} q^(n*(n+1)) / (1-q)^n ).
%Y A321481 Cf. A063978.
%K A321481 nonn
%O A321481 0,3
%A A321481 _Joerg Arndt_, Nov 11 2018