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A319931 a(n) = -(1/120)*n*(n - 3)*(n - 6)*(n^2 - 21*n + 8).

%I A319931 #10 Oct 21 2022 21:38:04
%S A319931 0,1,2,0,-4,-6,0,21,64,135,238,374,540,728,924,1107,1248,1309,1242,
%T A319931 988,476,-378,-1672,-3519,-6048,-9405,-13754,-19278,-26180,-34684,
%U A319931 -45036,-57505,-72384,-89991,-110670,-134792,-162756,-194990,-231952,-274131,-322048,-376257
%N A319931 a(n) = -(1/120)*n*(n - 3)*(n - 6)*(n^2 - 21*n + 8).
%H A319931 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A319931 a(n) = [x^5] DedekindEta(x)^n.
%F A319931 a(n) = A319933(n, 5).
%F A319931 From _Chai Wah Wu_, Jul 27 2022: (Start)
%F A319931 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.
%F A319931 G.f.: x*(-7*x^4 + 6*x^3 + 3*x^2 - 4*x + 1)/(x - 1)^6. (End)
%p A319931 a := n -> -(1/120)*n*(n-3)*(n-6)*(n^2-21*n+8):
%p A319931 seq(a(n), n=0..41);
%o A319931 (PARI) a(n)=-n*(n-3)*(n-6)*(n^2-21*n+8)/120 \\ _Charles R Greathouse IV_, Oct 21 2022
%Y A319931 Cf. A000012 (m=0), A001489 (m=1), A080956 (m=2), A167541 (m=3), A319930 (m=4), this sequence (m=5), A319932 (m=6).
%Y A319931 Cf. A319933.
%K A319931 sign,easy
%O A319931 0,3
%A A319931 _Peter Luschny_, Oct 02 2018