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A386898 a(n) = Sum_{k=0..n} binomial(5*n+1,k) * binomial(5*n-k,n-k).

%I A386898 #11 Aug 07 2025 08:35:07
%S A386898 1,11,199,4031,85919,1885311,42154111,955020287,21847988735,
%T A386898 503573013503,11675986431999,272033089535999,6363380561141759,
%U A386898 149354395882487807,3515589114309115903,82957940541503045631,1961823306198598418431,46482660516543479939071
%N A386898 a(n) = Sum_{k=0..n} binomial(5*n+1,k) * binomial(5*n-k,n-k).
%F A386898 a(n) = [x^n] (1+x)^(5*n+1)/(1-x)^(4*n+1).
%F A386898 a(n) = [x^n] 1/((1-x) * (1-2*x)^(4*n+1)).
%F A386898 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(5*n+1,k).
%F A386898 a(n) = Sum_{k=0..n} 2^k * binomial(4*n+k,k).
%F A386898 a(n) = binomial(5*n, n)*hypergeom([-1-5*n, -n], [-5*n], -1). - _Stefano Spezia_, Aug 07 2025
%o A386898 (PARI) a(n) = sum(k=0, n, binomial(5*n+1, k)*binomial(5*n-k, n-k));
%Y A386898 Cf. A386812, A386895, A386896, A386897.
%Y A386898 Cf. A178792, A383326, A383716.
%K A386898 nonn
%O A386898 0,2
%A A386898 _Seiichi Manyama_, Aug 07 2025