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A059823 Expansion of series related to Liouville's Last Theorem: g.f. sum_{t>0} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^6 *product_{i=1..t} (1-x^i) ). 1

%I

%S 0,1,7,27,83,202,455,889,1682,2892,4894,7694,12090,17822,26411,37206,

%T 52730,71447,97984,128714,171421,220064,285963,359204,458506,565347,

%U 708665,862163,1064302,1276474,1558090,1845874,2226044,2614188

%N Expansion of series related to Liouville's Last Theorem: g.f. sum_{t>0} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^6 *product_{i=1..t} (1-x^i) ).

%H G. E. Andrews, <a href="http://www.mat.univie.ac.at/~slc/s/s42andrews.html">Some debts I owe</a>, Seminaire Lotharingien Combinatoire, Paper B42a, Issue 42, 2000; see (7.4).

%p Mk := proc(k) -1*add( (-1)^n*q^(n*(n+1)/2)/(1-q^n)^k/mul(1-q^i,i=1..n), n=1..101): end; # with k=6

%Y Cf. A000005 (k=1), A059819 (k=2), A059820 (k=3), ..., A059825 (k=8).

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Feb 24 2001

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)