OFFSET
1,2
FORMULA
a(n) ~ (Pi^(3/2) + 2*sqrt(Pi)*log(1 + sqrt(2))) * 2^(2*n - 2) * n^(n - 1/4) / (Gamma(1/4) * exp(n)). - Vaclav Kotesovec, Jan 02 2020
From Peter Bala, Mar 21 2024: (Start)
a(n) = Product_{k = 0..n} (4*k + 1) * Sum_{k = 0..n} (-1)^k/(4*k + 1).
a(n) = 4*a(n-1) + (4*n - 3)^2*a(n-2) with a(0) = 1 and a(1) = 4.
MAPLE
a := proc(n) option remember; if n = 0 then 1 elif n = 1 then 4 else 4*a(n-1) + (4*n - 3)^2*a(n-2) end if; end:
seq(a(n), n = 0..20);
MATHEMATICA
Table[Product[4*k - 3, {k, 1, n}] * Sum[(-1)^(k+1)/(4*k - 3), {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jan 02 2020 *)
PROG
(PARI) a(n) = prod(k=1, n, 4*k-3)*sum(k=1, n, (-1)^(k+1)/(4*k-3)); \\ Michel Marcus, Jul 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Jul 06 2019
STATUS
approved