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A307376 a(n) = 1/n! * Sum_{k=0..n} (2*n+k)!/((n-k)!*k!*2^k).

%I A307376 #14 Apr 06 2019 10:21:40
%S A307376 1,5,81,2330,97405,5360607,366432990,29948982492,2849278444155,
%T A307376 309333396512855,37741150862494651,5112458462852223210,
%U A307376 761358344010536141506,123636426598733578925150,21742842987398075489784900,4116720379411455407932693320,834934865669512891440715729125
%N A307376 a(n) = 1/n! * Sum_{k=0..n} (2*n+k)!/((n-k)!*k!*2^k).
%H A307376 Seiichi Manyama, <a href="/A307376/b307376.txt">Table of n, a(n) for n = 0..313</a>
%F A307376 a(n) = (-1)^n * A144505(2*n+1, n).
%F A307376 a(n) ~ 3^(3*n + 1/2) * n^(n - 1/2) / (sqrt(Pi) * 2^(n + 1/2) * exp(n - 2/3)). - _Vaclav Kotesovec_, Apr 06 2019
%t A307376 Table[Sum[(2*n + k)!/((n - k)!*k!*2^k)/n!, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 06 2019 *)
%o A307376 (PARI) {a(n) = sum(k=0, n, (2*n+k)!/((n-k)!*k!*2^k))/n!}
%Y A307376 Cf. A144505.
%K A307376 nonn
%O A307376 0,2
%A A307376 _Seiichi Manyama_, Apr 06 2019