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A124161
a(n) = n*(n-1)*(n^3 + 21*n^2 - 4*n + 96)/120.
1
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
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]
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 03 2006
STATUS
approved