OFFSET
1,7
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
From Robert Israel, Jul 16 2020: (Start)
a(n) = (n - 5)^2*(n - 4)^2*(n - 3)^2*(n - 2)^2*(n - 1)^2*(2*n - 6)/86400.
G.f.: (1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)*x^6/(1 - x)^12. (End)
From Amiram Eldar, Jun 16 2026: (Start)
Sum_{n>=6} 1/a(n) = 2700*zeta(3) - 103825/32.
Sum_{n>=6} (-1)^n/a(n) = 2025*zeta(3) + 12800*log(2) - 361775/32. (End)
MAPLE
seq((n - 5)^2*(n - 4)^2*(n - 3)^2*(n - 2)^2*(n - 1)^2*(2*n - 6)/86400, n=1..50); # Robert Israel, Jul 16 2020
MATHEMATICA
A132464[n_] := (n-5)^2*(n-4)^2*(n-3)^3*(n-2)^2*(n-1)^2/43200;
Array[A132464, 30] (* Paolo Xausa, Jun 03 2026 *)
(* Alternative: *)
LinearRecurrence[{12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {0, 0, 0, 0, 0, 1, 48, 735, 6272, 37044, 169344, 640332}, 30] (* Harvey P. Dale, Jun 04 2026 *)
PROG
(PARI) a(n)=(n-5)^2*(n-4)^2*(n-3)^3*(n-2)^2*(n-1)^2/43200 \\ Charles R Greathouse IV, Jun 03 2026
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007
STATUS
approved