A370914 a(n) = n * (n + 4) * (n + 8).

0, 45, 120, 231, 384, 585, 840, 1155, 1536, 1989, 2520, 3135, 3840, 4641, 5544, 6555, 7680, 8925, 10296, 11799, 13440, 15225, 17160, 19251, 21504, 23925, 26520, 29295, 32256, 35409, 38760, 42315, 46080, 50061, 54264, 58695, 63360, 68265, 73416, 78819, 84480

Offset: 0

Author

Peter Luschny, Mar 06 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A370915 (case n=3).

Programs

Maple

a := n -> n * (n + 4) * (n + 8): seq(a(n), n = 0..40);

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {0, 45, 120, 231}, 41] (* Hugo Pfoertner, Mar 06 2024 *)

Formula

a(n) = 64*Pochhammer(n/4, 3).

a(n) = n^3 + 12*n^2 + 32*n.

a(n) = [x^n] 3*x*(7*x^2 - 20*x + 15)/(x - 1)^4.

a(n) = Sum_{k=0..3} Stirling1(3, k)*(-4)^(3 - k)*n^k.

From Amiram Eldar, Oct 03 2024: (Start)

Sum_{n>=1} 1/a(n) = 1217/26880.

Sum_{n>=1} (-1)^(n+1)/a(n) = 149/8960. (End)