A140354 a(n) = binomial(n+9,9)*2^n.

1, 20, 220, 1760, 11440, 64064, 320320, 1464320, 6223360, 24893440, 94595072, 343982080, 1203937280, 4074864640, 13388840960, 42844291072, 133888409600, 409541017600, 1228623052800, 3621204787200, 10501493882880, 30004268236800

Offset

0,2

Comments

Number of 9D hypercubes in an (n+9)-dimensional hypercube. - Zerinvary Lajos, Jan 29 2010; corrected by Michel Marcus, Jan 10 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Milan Janjic and Boris Petkovic, A Counting Function, arXiv:1301.4550 [math.CO], 2013.

Index entries for linear recurrences with constant coefficients, signature (20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024).

Formula

a(n) = A038207(n+9,9).

G.f.: 1/(1-2*x)^10. - Harvey P. Dale, Jul 18 2011

a(0)=1, a(1)=20, a(2)=220, a(3)=1760, a(4)=11440, a(5)=64064, a(6)=320320, a(7)=1464320, a(8)=6223360, a(9)=24893440; for n>9, a(n) = 20*a(n-1) - 180*a(n-2) + 960*a(n-3) - 3360*a(n-4) + 8064*a(n-5) - 13440*a(n-6) + 15360*a(n-7) - 11520*a(n-8) + 5120*a(n-9) - 1024*a(n-10). - Harvey P. Dale, Jul 18 2011

a(n) = 2*a(n-1) + A140325(n-1). - Ruskin Harding, May 13 2013

a(n) = Sum_{i=9..n+9} binomial(i,9)*binomial(n+9,i). - Bruno Berselli, Mar 23 2018

From Amiram Eldar, Jan 07 2022: (Start)

Sum_{n>=0} 1/a(n) = 18*log(2) - 1599/140.

Sum_{n>=0} (-1)^n/a(n) = 118098*log(3/2) - 6703713/140. (End)

Example

For n=6, a(6) = 1*5005 + 10*3003 + 55*1365 + 220*455 + 715*105 + 2002*15 + 5005*1 = 320320.

Maple

seq(binomial(n+9, 9)*2^n, n=0..23);

Mathematica

Table[Binomial[n + 9, 9] 2^n, {n, 0, 20}] (* Zerinvary Lajos, Jan 29 2010 *)
CoefficientList[Series[1/(1-2x)^10, {x, 0, 30}], x] (* Harvey P. Dale, Jul 18 2011 *)

Prog

(Sage) [lucas_number2(n, 2, 0)*binomial(n, 9)/512 for n in range(9, 31)] # Zerinvary Lajos, Mar 10 2009
(PARI) a(n)=binomial(n+9, 9)<<n \\ Charles R Greathouse IV, Jul 18 2011
(Magma) [2^n*Binomial(n+9, 9): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011

Crossrefs

Cf. A038207, A140325.

Sequence in context: A140236 A341371 A004411 * A155673 A000833 A302661

Adjacent sequences: A140351 A140352 A140353 * A140355 A140356 A140357

Keyword

nonn,easy

Author

Zerinvary Lajos, Jun 23 2008

Status

approved