A112415 a(n) = C(1+n,1) * C(2+n,1) * C(4+n,2).

12, 60, 180, 420, 840, 1512, 2520, 3960, 5940, 8580, 12012, 16380, 21840, 28560, 36720, 46512, 58140, 71820, 87780, 106260, 127512, 151800, 179400, 210600, 245700, 285012, 328860, 377580, 431520, 491040, 556512, 628320, 706860, 792540, 885780, 987012, 1096680

Offset: 0

Author

Zerinvary Lajos, Dec 09 2005

Keywords

• easy
• nonn

Examples

			n=0: C(1+0,1)*C(2+0,1)*C(4+0,2) = C(1,1)*C(2,1)*C(4,2) = 1*2*6 = 12;
n=10: C(1+10,1)*C(2+10,1)*C(4+10,2) = C(11,1)*C(12,1)*C(14,2) = 11*12*91 = 12012.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..680
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000332, A033486.

Programs

Magma

[(n+1)*(n+2)*(n+3)*(n+4)/2: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

Mathematica

Table[(n+1)(n+2)Binomial[4+n,2],{n,0,30}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{12,60,180,420,840},31] (* Harvey P. Dale, Jul 24 2011 *)

Formula

From R. J. Mathar, Aug 15 2008: (Start)

a(n) = (n+1)*(n+2)*(n+3)*(n+4)/2 = A033486(n+1) = 12*A000332(n+4).

O.g.f.: 12/(1-x)^5. (End)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=12, a(1)=60, a(2)=180, a(3)=420, a(4)=840. - Harvey P. Dale, Jul 24 2011

From Amiram Eldar, Sep 04 2022: (Start)

Sum_{n>=0} 1/a(n) = 1/9.

Sum_{n>=0} (-1)^n/a(n) = 8*(3*log(2)-2)/9. (End)