OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = [x^5] JacobiTheta3(x)^n.
a(n) = A319574(n,5).
From Colin Barker, Oct 02 2018: (Start)
G.f.: 8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6.
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.
(End)
MAPLE
a := n -> (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9):
seq(a(n), n=0..41);
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 8, 24, 48, 112}, 50] (* Paolo Xausa, Feb 20 2024 *)
PROG
(PARI) concat([0, 0], Vec(8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6 + O(x^40))) \\ Colin Barker, Oct 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 01 2018
STATUS
approved