%I #12 Jan 02 2020 04:29:34

%S 1,4,97,1064,32289,598380,22574145,593534160,26957380545,920377787220,

%T 48996867845025,2059752490500600,125880489657907425,

%U 6289366704447815100,434143177716332484225,25139306218115649924000,1934812150723967345546625,127427485507344478670350500

%N a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 4k-3 for k = 1,2,3,...

%H Andrew Howroyd, <a href="/A024384/b024384.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) ~ sqrt(Pi) * (8 - sqrt(2)*Pi - 2^(3/2) * log(1 + sqrt(2))) * 2^(2*n - 1/2) * n^(n + 3/4) / (Gamma(1/4) * exp(n)). - _Vaclav Kotesovec_, Jan 02 2020

%t Table[Product[4*k - 3, {k, 1, n+1}] * Sum[(-1)^k/(4*k - 3), {k, 2, n+1}], {n, 1, 20}] (* _Vaclav Kotesovec_, Jan 02 2020 *)

%o (PARI) a(n)={my(s=vector(n+1, k, 4*k-3)); vecprod(s)*sum(k=2, #s, (-1)^k/s[k])} \\ _Andrew Howroyd_, Jan 01 2020

%Y Cf. A024383, A024397.

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Extra initial term removed and a(11) and beyond added by _Andrew Howroyd_, Jan 01 2020