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A162668 a(n) = n*(n+1)*(n+2)*(n+3)/3. 3
0, 8, 40, 120, 280, 560, 1008, 1680, 2640, 3960, 5720, 8008, 10920, 14560, 19040, 24480, 31008, 38760, 47880, 58520, 70840, 85008, 101200, 119600, 140400, 163800, 190008, 219240, 251720, 287680, 327360, 371008, 418880, 471240, 528360, 590520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Diego Marques, The order of appearance of the product of consecutive Lucas numbers, Fibonacci Quarterly, 51 (2013), 38-43. - From N. J. A. Sloane, Mar 06 2013

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

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

a(n) = 8*A000332(n+3).

G.f.: 8*x/(1-x)^5. (End)

For n>0 a(n)=1/(Integral_{x=0..Pi/2} (sin(x))^7*(cos(x))^(2*n-1)). - Francesco Daddi, Aug 02 2011

E.g.f.: x*(24 +36*x +12*x^2 +x^3)*exp(x)/3. - G. C. Greubel, Aug 27 2019

MAPLE

seq(8*binomial(n+3, 4), n=0..40); # G. C. Greubel, Aug 27 2019

MATHEMATICA

Table[n*(n+1)*(n+2)*(n+3)/3, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2009, modified by G. C. Greubel, Aug 27 2019 *)

8*Binomial[Range[40]+2, 4] (* G. C. Greubel, Aug 27 2019 *)

PROG

(MAGMA) [n*(n+1)*(n+2)*(n+3)/3: n in [0..40] ];

(PARI) binomial(n+3, 4)/8 \\ Charles R Greathouse IV, Jan 11 2012

(Sage) [8*binomial(n+3, 4) for n in (0..40)] # G. C. Greubel, Aug 27 2019

(GAP) List([0..40], n-> 8*Binomial(n+3, 4)); # G. C. Greubel, Aug 27 2019

CROSSREFS

Cf. A162669.

Sequence in context: A143943 A135796 A105374 * A227733 A191903 A028596

Adjacent sequences:  A162665 A162666 A162667 * A162669 A162670 A162671

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jul 10 2009

EXTENSIONS

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

STATUS

approved

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)