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A105947 a(n) = C(n+6,n)*C(n+4,4). 0

%I #16 Sep 08 2022 08:15:09

%S 1,35,420,2940,14700,58212,194040,566280,1486485,3578575,8016008,

%T 16893240,33786480,64574160,118605600,210327264,361499985,604167795,

%U 984569740,1568220500,2446423980,3744526500,5632263000,8336601000,12157543125,17487410031,24834191760

%N a(n) = C(n+6,n)*C(n+4,4).

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F G.f.: (15*x^4+80*x^3+90*x^2+24*x+1) / (1-x)^11. [_Colin Barker_, Jan 28 2013]

%F From _Wesley Ivan Hurt_, Jan 27 2022: (Start)

%F a(n) = (17280 + 78336*n + 152376*n^2 + 167780*n^3 + 116150*n^4 + 52983*n^5 +

%F 16173*n^6 + 3270*n^7 + 420*n^8 + 31*n^9 + n^10)/17280.

%F a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). (End)

%F From _Amiram Eldar_, Sep 08 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 224*Pi^2 - 55244/25.

%F Sum_{n>=0} (-1)^n/a(n) = 12*Pi^2 + 512*log(2)/5 - 4711/25. (End)

%e If n=0 then C(0+6,0)*C(0+4,4) = C(6,0)*C(4,4) = 1*1 = 1.

%e If n=10 then C(10+6,10)*C(10+4,4) = C(16,10)*C(14,4) = 8008*1001 = 8016008.

%t Table[Binomial[n+6,n]Binomial[n+4,4],{n,0,30}] (* or *) LinearRecurrence[ {11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,35,420,2940,14700,58212,194040,566280,1486485,3578575,8016008},30] (* _Harvey P. Dale_, May 21 2014 *)

%Y Cf. A062196.

%K easy,nonn

%O 0,2

%A _Zerinvary Lajos_, Apr 27 2005

%E Terms from a(8) onwards corrected by _Colin Barker_, Jan 28 2013

%E Second example corrected by _Colin Barker_, Jan 28 2013

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)