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A276489 a(n) = 25^(n+1)*Gamma(n+8/5)/Gamma(3/5).

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%I A276489 #17 Jan 30 2020 21:29:17
%S A276489 15,600,39000,3510000,403650000,56511000000,9324315000000,
%T A276489 1771619850000000,380898267750000000,91415584260000000000,
%U A276489 24225129828900000000000,7025287650381000000000000,2212965609870015000000000000,752408307355805100000000000000,274629032184868861500000000000000
%N A276489 a(n) = 25^(n+1)*Gamma(n+8/5)/Gamma(3/5).
%F A276489 E.g.f.: 15/(1 - 25*x)^(8/5).
%F A276489 D-finite with recurrence: a(n) = 5*(5*n + 3)*a(n - 1), a(0)=15.
%F A276489 a(n) = Product_{k=0..n} 5*(5*k + 3).
%F A276489 a(n) = Product_{k=0..n} 5*A016885(k).
%F A276489 a(n) ~ sqrt(2*Pi)*25^(n+1)*n^(n+11/10)/(Gamma(3/5)*exp(n)).
%F A276489 Sum_{n>=0} 1/a(n) = exp(1/25)*(Gamma(3/5) - Gamma(3/5, 1/25))/5^(4/5)
%F A276489 = 0.06835926175445652444604..., where Gamma(a, x) is the incomplete Gamma function.
%e A276489 a(0) = (1+2+3+4+5) = 15;
%e A276489 a(1) = (1+2+3+4+5)*(6+7+8+9+10) = 600;
%e A276489 a(2) = (1+2+3+4+5)*(6+7+8+9+10)*(11+12+13+14+15) = 39000, etc.
%t A276489 FullSimplify[Table[25^(n + 1) (Gamma[n + 8/5]/Gamma[3/5]), {n, 0, 14}]]
%o A276489 (PARI) a(n) = prod(k=0, n, 5*(5*k + 3)); \\ _Michel Marcus_, Sep 06 2016
%Y A276489 Cf. A016885, A268730.
%K A276489 nonn,easy
%O A276489 0,1
%A A276489 _Ilya Gutkovskiy_, Sep 05 2016