A319932 a(n) = (1/720)*n*(n - 10)*(n - 1)*(n^3 - 34*n^2 + 181*n - 144).

0, 0, -2, -7, -10, -5, 11, 35, 56, 54, 0, -143, -418, -871, -1547, -2485, -3712, -5236, -7038, -9063, -11210, -13321, -15169, -16445, -16744, -15550, -12220, -5967, 4158, 19285, 40745, 70091, 109120, 159896, 224774, 306425, 407862, 532467, 684019, 866723

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

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

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

G.f.: -x^2*(2 - 7*x + 3*x^2 + 12*x^3 - 11*x^4)/(1 - x)^7. - Andrew Howroyd, Nov 06 2025

Maple

a := n -> (1/720)*n*(n-10)*(n-1)*(n^3-34*n^2+181*n-144);
seq(a(n), n=0..39);

Mathematica

Table[(n(n-10)(n-1)(n^3-34n^2+181n-144))/720, {n, 0, 40}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, -2, -7, -10, -5, 11}, 40] (* Harvey P. Dale, Jan 01 2026 *)

Prog

(PARI) a(n)=n*(n-10)*(n-1)*(n^3-34*n^2+181*n-144)/720 \\ Charles R Greathouse IV, May 26 2026

Crossrefs

Cf. A000012 (m=0), A001489 (m=1), A080956 (m=2), A167541 (m=3), A319930 (m=4), A319931 (m=5), this sequence (m=6).

Cf. A319933.

Sequence in context: A042157 A012937 A022414 * A236243 A024831 A362861

Adjacent sequences: A319929 A319930 A319931 * A319933 A319934 A319935

Keyword

sign,easy,changed

Author

Peter Luschny, Oct 02 2018

Status

approved