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a(n) = C(5+2*n,5+n)*C(10+2*n,0+n).
1

%I #11 Sep 09 2024 22:43:07

%S 1,84,3276,92400,2187900,46558512,923410488,17439488352,317907339750,

%T 5644249611000,98209943231400,1682207622669600,28457345616827400

%N a(n) = C(5+2*n,5+n)*C(10+2*n,0+n).

%H Robert Israel, <a href="/A114253/b114253.txt">Table of n, a(n) for n = 0..828</a>

%F From _Robert Israel_, Jan 11 2019: (Start)

%F (n+1)^2*(11+n)*a(n+1)=4*(7+2*n)*(3+n)*(11+2*n)*a(n).

%F a(n) ~ 32768*16^n/(Pi*n). (End)

%e If n=1 then C(5+2*1,5+1)*C(10+2*1,0+1) = C(7,6)*C(12,1) = 7*12 = 84.

%e If n=11 then C(5+2*n,5+n)*C(10+2*n,0+n) = C(27,16)*C(32,11) = 13037895*129024480 = 1682207622669600.

%p seq(binomial(5+2*n,5+n)*binomial(10+2*n,n),n=0..30); # _Robert Israel_, Jan 11 2019

%Y Cf. A062190.

%K easy,nonn

%O 0,2

%A _Zerinvary Lajos_, Feb 04 2006