A162669 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5.

0, 144, 1008, 4032, 12096, 30240, 66528, 133056, 247104, 432432, 720720, 1153152, 1782144, 2673216, 3907008, 5581440, 7814016, 10744272, 14536368, 19381824, 25502400, 33153120, 42625440, 54250560, 68402880, 85503600, 106024464, 130491648, 159489792, 193666176

Offset: 0

Author

Vincenzo Librandi, Jul 10 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000579.

Programs

GAP

List([0..30], n-> 144*Binomial(n+5, 6)); # G. C. Greubel, Aug 27 2019

Magma

[n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5: n in [1..30]]; // Vincenzo Librandi, Mar 05 2012

Maple

seq(144*binomial(n+5,6), n = 0..30); # G. C. Greubel, Aug 27 2019

Mathematica

CoefficientList[Series[144*x/(1-x)^7,{x,0,30}],x] (* Vincenzo Librandi, Mar 05 2012 *)
Table[(Times@@(n+Range[0,5]))/5,{n,0,30}] (* Harvey P. Dale, Jul 01 2019 *)
144*Binomial[Range[30] +4, 6] (* G. C. Greubel, Aug 27 2019 *)

PARI

vector(30, n, 144*binomial(n+4,6)) \\ G. C. Greubel, Aug 27 2019

Sage

[144*binomial(n+5,6) for n in (0..30)] # G. C. Greubel, Aug 27 2019

Formula

From R. J. Mathar, Jul 13 2009: (Start)

a(n) = 144 * A000579(n+5).

G.f.: 144*x/(1-x)^7. (End)

E.g.f.: x*(720 +1800*x +1200*x^2 +300*x^3 +30*x^4 +x^5)*exp(x)/5. - G. C. Greubel, Aug 27 2019

From Amiram Eldar, Jan 09 2022: (Start)

Sum_{n>=1} 1/a(n) = 1/120.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/3 - 661/720. (End)

Extensions

Definition factorized, offset corrected by R. J. Mathar, Jul 13 2009