cp's OEIS Frontend

A024384 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,...

%I A024384 #12 Jan 02 2020 04:29:34
%S A024384 1,4,97,1064,32289,598380,22574145,593534160,26957380545,920377787220,
%T A024384 48996867845025,2059752490500600,125880489657907425,
%U A024384 6289366704447815100,434143177716332484225,25139306218115649924000,1934812150723967345546625,127427485507344478670350500
%N A024384 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 A024384 Andrew Howroyd, <a href="/A024384/b024384.txt">Table of n, a(n) for n = 1..100</a>
%F A024384 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 A024384 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 A024384 (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 A024384 Cf. A024383, A024397.
%K A024384 nonn
%O A024384 1,2
%A A024384 _Clark Kimberling_
%E A024384 Extra initial term removed and a(11) and beyond added by _Andrew Howroyd_, Jan 01 2020