A104475 a(n) = binomial(n+4,4) * binomial(n+8,4).

70, 630, 3150, 11550, 34650, 90090, 210210, 450450, 900900, 1701700, 3063060, 5290740, 8817900, 14244300, 22383900, 34321980, 51482970, 75710250, 109359250, 155405250, 217567350, 300450150, 409704750, 552210750, 736281000, 971890920, 1270934280, 1647507400, 2118223800

Offset

0,1

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = 70*A000581(n-8). - Michel Marcus, Jul 31 2015

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 4/245.

Sum_{n>=0} (-1)^n/a(n) = 512*log(2)/35 - 37216/3675. (End)

Example

a(0): C(0+4,4)*C(0+8,4) = C(4,4)*C(8,4) = 1*70 = 70.
a(7): C(5+4,4)*C(5+8,4) = C(9,4)*(13,4) = 126*715 = 90090.

Maple

A104475:=n->binomial(n+4, 4)*binomial(n+8, 4): seq(A104475(n), n=0..40); # Wesley Ivan Hurt, Jan 29 2017

Mathematica

f[n_] := Binomial[n + 4, 4]Binomial[n + 8, 4]; Table[ f[n], {n, 0, 25}] (* Robert G. Wilson v, Apr 20 2005 *)

Prog

(PARI) vector(30, n, n--; binomial(n+4, 4)*binomial(n+8, 4)) \\ Michel Marcus, Jul 31 2015
(Magma) [Binomial(n+4, 4)*Binomial(n+8, 4): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015

Crossrefs

Cf. A000581.

Sequence in context: A229576 A234556 A183715 * A169712 A235488 A199829

Adjacent sequences: A104472 A104473 A104474 * A104476 A104477 A104478

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 18 2005

Extensions

More terms from Robert G. Wilson v, Apr 20 2005

Status

approved