OFFSET
0,3
COMMENTS
Arises in studying the Goldbach conjecture.
LINKS
Matthew House, Table of n, a(n) for n = 0..10000
P. A. MacMahon, Properties of prime numbers deduced from the calculus of symmetric functions, Proc. London Math. Soc., 23 (1923), 290-316. [Coll. Papers, II, pp. 354-382] [See p. 301]
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: x^2*(3-3*x+3*x^2-2*x^3)/(1-x)^6. - Matthew House, Jan 16 2017
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. - Colin Barker, Jan 16 2017
MATHEMATICA
Table[n(n-1)(n^3+21n^2-4n+96)/120, {n, 0, 50}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 3, 15, 48, 121}, 50] (* Harvey P. Dale, Nov 26 2022 *)
PROG
(PARI) concat(vector(2), Vec(x^2*(3-3*x+3*x^2-2*x^3) / (1-x)^6 + O(x^40))) \\ Colin Barker, Jan 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 03 2006
STATUS
approved