A319931 - OEIS

%I #10 Oct 21 2022 21:38:04

%S 0,1,2,0,-4,-6,0,21,64,135,238,374,540,728,924,1107,1248,1309,1242,

%T 988,476,-378,-1672,-3519,-6048,-9405,-13754,-19278,-26180,-34684,

%U -45036,-57505,-72384,-89991,-110670,-134792,-162756,-194990,-231952,-274131,-322048,-376257

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = [x^5] DedekindEta(x)^n.

%F a(n) = A319933(n, 5).

%F From _Chai Wah Wu_, Jul 27 2022: (Start)

%F 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 G.f.: x*(-7*x^4 + 6*x^3 + 3*x^2 - 4*x + 1)/(x - 1)^6. (End)

%p a := n -> -(1/120)*n*(n-3)*(n-6)*(n^2-21*n+8):

%p seq(a(n), n=0..41);

%o (PARI) a(n)=-n*(n-3)*(n-6)*(n^2-21*n+8)/120 \\ _Charles R Greathouse IV_, Oct 21 2022

%Y Cf. A000012 (m=0), A001489 (m=1), A080956 (m=2), A167541 (m=3), A319930 (m=4), this sequence (m=5), A319932 (m=6).

%Y Cf. A319933.

%K sign,easy

%O 0,3

%A _Peter Luschny_, Oct 02 2018