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a(n) = C(n+4,4)*C(n+6,4).
1

%I #10 Sep 06 2022 03:00:32

%S 15,175,1050,4410,14700,41580,103950,235950,495495,975975,1821820,

%T 3248700,5569200,9224880,14825700,23197860,35441175,52997175,77729190,

%U 112015750,158858700,222007500,306101250,416830050,561117375,747325215,985483800,1287547800

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

%H Harvey P. Dale, <a href="/A107395/b107395.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

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

%F Sum_{n>=0} 1/a(n) = 16*Pi^2 - 3946/25.

%F Sum_{n>=0} (-1)^n/a(n) = 1776/25 - 512*log(2)/5. (End)

%e If n=0 then C(0+4,4)*C(0+6,4) = C(4,4)*C(6,4) = 1*15 = 15.

%e If n=9 then C(9+4,4)*C(9+6,4) = C(13,4)*C(15,4) = 715*1365 = 975975.

%t Table[Binomial[n+4,4]Binomial[n+6,4],{n,0,30}] (* _Harvey P. Dale_, Jun 07 2019 *)

%Y Cf. A062196.

%K easy,nonn

%O 0,1

%A _Zerinvary Lajos_, May 25 2005

%E More terms from _Harvey P. Dale_, Jun 07 2019