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

0, 1, 2, 0, -4, -6, 0, 21, 64, 135, 238, 374, 540, 728, 924, 1107, 1248, 1309, 1242, 988, 476, -378, -1672, -3519, -6048, -9405, -13754, -19278, -26180, -34684, -45036, -57505, -72384, -89991, -110670, -134792, -162756, -194990, -231952, -274131, -322048, -376257

Offset: 0

Author

Peter Luschny, Oct 02 2018

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

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

Cf. A319933.

Programs

Maple

a := n -> -(1/120)*n*(n-3)*(n-6)*(n^2-21*n+8):
seq(a(n), n=0..41);

PARI

a(n)=-n*(n-3)*(n-6)*(n^2-21*n+8)/120 \\ Charles R Greathouse IV, Oct 21 2022

Formula

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

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

From Chai Wah Wu, Jul 27 2022: (Start)

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.

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