%I #10 Feb 20 2020 05:01:34

%S -1,1,6,78,1576,43320,1507824,63549808,3145681536,178865283456,

%T 11488065875200,822528662774016,64957295774721024,5609010346397166592,

%U 525718830294548330496,53154054477553828608000,5766597997397483718344704,668177890990349738366042112,82355042760252520538828242944

%N a(n) = -(-1)^n * n! * hypergeometric1F1(1 - n, 2, 4*n).

%H Vaclav Kotesovec, <a href="/A332680/b332680.txt">Table of n, a(n) for n = 0..336</a>

%F A302112(n) = (A332679(n) - 2*n*a(n)) * binomial(2*n, n) / 2^n.

%F a(n) ~ c * n^(n - 5/6) * exp(n), where c = Gamma(1/3) / (2^(11/6) * 3^(1/6) * sqrt(Pi)) = 0.3531663187295...

%t Table[-(-1)^n * n! * Hypergeometric1F1[1 - n, 2, 4*n], {n, 0, 20}]

%t Join[{-1}, Table[n! * Sum[(-1)^(n-k+1) * Binomial[n-1, k] * (4*n)^k / (k+1)!, {k, 0, n-1}], {n, 1, 20}]]

%Y Cf. A302112, A332679.

%K sign

%O 0,3

%A _Vaclav Kotesovec_, Feb 19 2020