OFFSET
0,2
COMMENTS
This sequence is c_11 in the 2015 paper of Cooper et al.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..819
S. Cooper, Ramanujan's theories of elliptic functions to alternative bases, and beyond, talk slides, Askey 80 Conference, 2013.
S. Cooper, J. Ge and D. Ye, Hypergeometric transformation formulas of degrees 3, 7, 11 and 23, Journal of Mathematical Analysis and Applications, Volume 421, Issue 2, 15 January 2015, Pages 1358-1376.
FORMULA
a(n) ~ c * d^n / (Pi*n)^(3/2), where d = 16.8275008141470347474718307386716769... is the real root of the equation -44 + 56*d - 20*d^2 + d^3 = 0 and c = 1.83051467150137478416073409831908489312609... is the positive real root of the equation -1331 - 1020*c^2 - 1936*c^4 + 704*c^6 = 0. - Vaclav Kotesovec, Apr 02 2017
MATHEMATICA
RecurrenceTable[{(n+1)^3*a[n+1] == 2*(2*n+1)*(5*n^2+5*n+2)*a[n] - 8*n*(7*n^2+1)*a[n-1] + 22*n*(n-1)*(2*n-1)*a[n-2], a[0]==1, a[1]==4, a[2]==28}, a, {n, 0, 20}] (* Vaclav Kotesovec, Apr 02 2017 *)
PROG
(Ruby)
def A284756(n)
a, b, c, i = 0, 0, 1, -1
ary = [0, 0]
while i < n
i += 1
j = 2 * (2 * i + 1) * (5 * i * i + 5 * i + 2) * c - 8 * i * (7 * i * i + 1) * b + 22 * i * (i - 1) * (2 * i - 1) * a
break if j % ((i + 1) ** 3) > 0
a, b, c = b, c, j / ((i + 1) ** 3)
ary << b
end
ary[2..-1]
end
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 02 2017
STATUS
approved