A124161 a(n) = n*(n-1)*(n^3 + 21*n^2 - 4*n + 96)/120.

0, 0, 3, 15, 48, 121, 261, 504, 896, 1494, 2367, 3597, 5280, 7527, 10465, 14238, 19008, 24956, 32283, 41211, 51984, 64869, 80157, 98164, 119232, 143730, 172055, 204633, 241920, 284403, 332601, 387066, 448384, 517176, 594099, 679847, 775152, 880785, 997557

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

Sequence in context: A135622 A316853 A061316 * A089580 A034564 A012203

Adjacent sequences: A124158 A124159 A124160 * A124162 A124163 A124164

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 03 2006

Status

approved