OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = [x^4] JacobiTheta3(x)^n.
a(n) = A319574(n,4).
From Colin Barker, Oct 02 2018: (Start)
G.f.: 2*x*(1 + x)*(1 - 4*x + 7*x^2) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. (End)
MAPLE
a := n -> (2/3)*n*(n^3 - 6*n^2 + 11*n - 3):
seq(a(n), n=0..38);
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 4, 6, 24}, 50] (* Paolo Xausa, Feb 20 2024 *)
PROG
(PARI) concat(0, Vec(2*x*(1 + x)*(1 - 4*x + 7*x^2) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Oct 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 01 2018
STATUS
approved