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A105939 a(n) = C(n+3,3)*C(n+6,3). 1
20, 140, 560, 1680, 4200, 9240, 18480, 34320, 60060, 100100, 160160, 247520, 371280, 542640, 775200, 1085280, 1492260, 2018940, 2691920, 3542000, 4604600, 5920200, 7534800, 9500400, 11875500, 14725620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the number of ordered pairs (A,B) of size 3 subsets of {1,2,...,n+6} such that A and B are disjoint. - Geoffrey Critzer, Sep 03 2013

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: 20/(1-x)^7. [Colin Barker, Jun 06 2012]

With offset = 6, E.g.f.: exp(x)*x^3/3!*x^3/3!. - Geoffrey Critzer, Sep 03 2013

a(n) = A000292(n+1)*A000292(n+4) = 20*A000579(n+6). - R. J. Mathar, Nov 30 2015

EXAMPLE

If n=0 then C(0+3,0)*C(0+6,3) = C(3,0)*C(6,3) = 1*20 = 20.

If n=8 then C(8+3,8)*C(8+6,3) = C(11,8)*C(14,3) = 165*364 = 60060.

MATHEMATICA

nn=25; f[x_]:=Exp[x](x^3/3!)^2; Range[0, nn]!CoefficientList[Series[a=f''''''[x], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 03 2013 *)

CROSSREFS

Cf. A062145.

Sequence in context: A264308 A236988 A134382 * A054389 A253003 A293932

Adjacent sequences:  A105936 A105937 A105938 * A105940 A105941 A105942

KEYWORD

easy,nonn

AUTHOR

Zerinvary Lajos, Apr 27 2005

EXTENSIONS

More terms from Geoffrey Critzer, Sep 03 2013

STATUS

approved

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Last modified July 18 07:10 EDT 2019. Contains 325134 sequences. (Running on oeis4.)