A319930 a(n) = (1/24)*n*(n - 1)*(n - 3)*(n - 14).

0, 0, 1, 0, -5, -15, -30, -49, -70, -90, -105, -110, -99, -65, 0, 105, 260, 476, 765, 1140, 1615, 2205, 2926, 3795, 4830, 6050, 7475, 9126, 11025, 13195, 15660, 18445, 21576, 25080, 28985, 33320, 38115, 43401, 49210, 55575, 62530, 70110, 78351, 87290, 96965

Offset

0,5

Links

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = [x^4] DedekindEta(x)^n.

a(n) = A319933(n, 4).

From Elmo R. Oliveira, Apr 11 2026: (Start)

G.f.: x^2*(1 - 5*x + 5*x^2)/(1 - x)^5.

E.g.f.: x^2*(x^2 - 12*x + 12)*exp(x)/24.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

Maple

a := n -> (1/24)*n*(n-1)*(n-3)*(n-14):
seq(a(n), n=0..44);

Mathematica

Table[(n(n-1)(n-3)(n-14))/24, {n, 0, 70}] (* Harvey P. Dale, Apr 29 2022 *)

Crossrefs

Cf. A000012 (m=0), A001489 (m=1), A080956 (m=2), A167541 (m=3), this sequence (m=4), A319931 (m=5), A319932 (m=6).

Cf. A319933.

Sequence in context: A285630 A078905 A059160 * A357690 A341984 A028895

Adjacent sequences: A319927 A319928 A319929 * A319931 A319932 A319933

Keyword

sign,easy

Author

Peter Luschny, Oct 02 2018

Status

approved