OFFSET
0,4
LINKS
Seiichi Manyama, 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^6] JacobiTheta3(x)^n.
a(n) = A319574(n,6).
From Colin Barker, Oct 02 2018: (Start)
G.f.: 8*x^3*(3 - 9*x + 9*x^2 + 5*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
(End)
MAPLE
a := n -> (4/45)*n*(n - 2)*(n - 1)*(n^3 - 12*n^2 + 47*n - 15):
seq(a(n), n=0..41);
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 24, 96, 240, 544}, 50] (* Paolo Xausa, Feb 20 2024 *)
PROG
(PARI) concat([0, 0, 0], Vec(8*x^3*(3 - 9*x + 9*x^2 + 5*x^3) / (1 - x)^7 + O(x^40))) \\ Colin Barker, Oct 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 01 2018
STATUS
approved