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A104678 a(n) = binomial(n+4,4) * binomial(n+9,4).

%I A104678 #22 Aug 30 2022 09:44:20
%S A104678 126,1050,4950,17325,50050,126126,286650,600600,1178100,2187900,
%T A104678 3879876,6613425,10892700,17409700,27096300,41186376,61289250,
%U A104678 89475750,128378250,181306125,252378126,346673250,470401750,631098000,837837000,1101476376,1434925800
%N A104678 a(n) =  binomial(n+4,4) * binomial(n+9,4).
%H A104678 <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 A104678 From _R. J. Mathar_, Nov 29 2015: (Start)
%F A104678 a(n) = A000332(n+4)*A000332(n+9).
%F A104678 G.f.: ( -126+84*x-36*x^2+9*x^3-x^4 ) / (x-1)^9. (End)
%F A104678 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104678 Sum_{n>=0} 1/a(n) = 9/980.
%F A104678 Sum_{n>=0} (-1)^n/a(n) = 1/140. (End)
%e A104678 If n=0 then C(0+4,0+0)*C(0+9,4) = C(4,0)*C(9,4) = 1*126 = 126.
%e A104678 If n=5 then C(5+4,5+0)*C(5+9,4) = C(9,5)*C(14,4) = 126*1001 = 126126.
%p A104678 A104678:=n->binomial(n+4,n)*binomial(n+9,4); seq(A104678(n), n=0..100); # _Wesley Ivan Hurt_, Dec 03 2013
%t A104678 Table[Binomial[n + 4, n] Binomial[n + 9, 4], {n, 0, 100}] (* _Wesley Ivan Hurt_, Dec 03 2013 *)
%Y A104678 Cf. A000332, A062190.
%K A104678 easy,nonn
%O A104678 0,1
%A A104678 _Zerinvary Lajos_, Apr 22 2005