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A107421 a(n) = C(n+6,6)*C(n+9,9). 1

%I #12 Sep 06 2022 02:59:47

%S 1,70,1540,18480,150150,924924,4624620,19631040,73002930,243343100,

%T 739763024,2078672960,5456516520,13495999440,31674284400,70950397056,

%U 152432493675,315413948850,630827897700,1223211990000,2305754601150,4235059471500,7595106655500

%N a(n) = C(n+6,6)*C(n+9,9).

%H T. D. Noe, <a href="/A107421/b107421.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

%F G.f.: (84*x^6+756*x^5+1890*x^4+1680*x^3+540*x^2+54*x+1)/(x-1)^16. - _Harvey P. Dale_, Jan 30 2013

%F From _Amiram Eldar_, Sep 06 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 11583*Pi^2 - 4481289621/39200.

%F Sum_{n>=0} (-1)^n/a(n) = 73728*log(2)/35 - 225*Pi^2/2 - 13673259/39200. (End)

%e If n=0 then C(0+6,6)*C(0+9,9) = C(6,6)*C(9,9) = 1*1 = 1.

%e If n=7 then C(7+6,6)*C(7+9,9) = C(13,6)*C(16,9) = 1716*11440 = 19631040.

%t Table[Binomial[n+6,6]Binomial[n+9,9],{n,0,30}] (* _Harvey P. Dale_, Jan 30 2013 *)

%o (PARI) for(n=0,29,print1(binomial(n+6,6)*binomial(n+9,9),","))

%Y Cf. A062145.

%K easy,nonn

%O 0,2

%A _Zerinvary Lajos_, May 26 2005

%E Corrected and extended by _Rick L. Shepherd_, May 27 2005

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)