A104677 a(n) = binomial(n+3,3)*binomial(n+8,3).

56, 336, 1200, 3300, 7700, 16016, 30576, 54600, 92400, 149600, 233376, 352716, 518700, 744800, 1047200, 1445136, 1961256, 2622000, 3458000, 4504500, 5801796, 7395696, 9338000, 11687000, 14508000, 17873856, 21865536, 26572700, 32094300, 38539200, 46026816

Offset

0,1

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

From R. J. Mathar, Nov 29 2015: (Start)

a(n) = A000292(n+1)*A000292(n+6) = 4*A033276(n+6).

G.f.: 4*(-14+14*x-6*x^2+x^3)/(x-1)^7. (End)

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 109/4900.

Sum_{n>=0} (-1)^n/a(n) = 48*log(2)/35 - 2291/2450. (End)

Example

If n=0 then C(0+3,0+0)*C(0+8,3) = C(3,0)*C(8,3) = 1*56 = 56.
If n=8 then C(8+3,8+0)*C(8+8,3) = C(11,8)*C(16,3) = 165*560 = 92400.

Mathematica

a[n_] :=  Binomial[n+3, 3] * Binomial[n+8, 3]; Array[a, 30, 0] (* Amiram Eldar, Aug 30 2022 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {56, 336, 1200, 3300, 7700, 16016, 30576}, 40] (* Harvey P. Dale, Jan 06 2023 *)

Crossrefs

Cf. A000292, A033276, A062190.

Sequence in context: A005912 A264581 A220202 * A156375 A219718 A296823

Adjacent sequences: A104674 A104675 A104676 * A104678 A104679 A104680

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 22 2005

Status

approved