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A105942 C(n+6,n)*C(n+9,6) 0
84, 1470, 12936, 77616, 360360, 1387386, 4624620, 13741728, 37165128, 92912820, 217273056, 479693760, 1007356896, 2024399916, 3912705720, 7303717344, 13213962300, 23241027810, 39841761960, 66720654000, 109363854600, 175763337750, 277386503940, 430459323840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f.: -((42*(x+1)*(x*(2*x+7)+2))/(x-1)^13). - Harvey P. Dale, Sep 14 2012

a(0)=84, a(1)=1470, a(2)=12936, a(3)=77616, a(4)=360360, a(5)=1387386, a(6)=4624620, a(7)=13741728, a(8)=37165128, a(9)=92912820, a(10)=217273056, a(11)=479693760, a(12)=1007356896, a(n)=13*a(n-1)- 78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+1716*a(n-7)- 1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - Harvey P. Dale, Sep 14 2012

EXAMPLE

If n=0 then C(0+6,0)*C(0+9,6)= C(6,0)*C(9,6)=1*84=84

If n=6 then C(6+6,6)*C(6+9,6)= C(12,6)*C(15,6)=924*5005=4624620

MATHEMATICA

Table[Binomial[n+6, n]Binomial[n+9, 6], {n, 0, 30}] (* or *) CoefficientList[ Series[-((42 (x+1) (x (2 x+7)+2))/(x-1)^13), {x, 0, 30}], x] (* Harvey P. Dale, Sep 14 2012 *)

CROSSREFS

Cf. A062145.

Sequence in context: A163592 A244910 A277784 * A219476 A008359 A166847

Adjacent sequences:  A105939 A105940 A105941 * A105943 A105944 A105945

KEYWORD

easy,nonn

AUTHOR

Zerinvary Lajos, Apr 27 2005

EXTENSIONS

Corrected and extended by Harvey P. Dale, Sep 14 2012

STATUS

approved

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)