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,...

1, 4, 97, 1064, 32289, 598380, 22574145, 593534160, 26957380545, 920377787220, 48996867845025, 2059752490500600, 125880489657907425, 6289366704447815100, 434143177716332484225, 25139306218115649924000, 1934812150723967345546625, 127427485507344478670350500

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A024383, A024397.

Sequence in context: A333539 A356808 A041275 * A368004 A320358 A180830

Adjacent sequences: A024381 A024382 A024383 * A024385 A024386 A024387

Keyword

nonn

Author

Clark Kimberling

Extensions

Extra initial term removed and a(11) and beyond added by Andrew Howroyd, Jan 01 2020

Status

approved