OFFSET
0,3
COMMENTS
a(n) = K(8,8; n)/8 with K(a,b; n) defined in a comment to A068763.
LINKS
Fung Lam, Table of n, a(n) for n = 0..750
FORMULA
a(n) = (8^n) * p(n, -7/8) with the row polynomials p(n, x) defined from array A068763.
a(n+1) = 8*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-32*x*(1-7*x)))/(16*x).
a(n) = (4^(n-1)*14^(1/2*n+1/2)*LegendreP(n+1,2/7*14^(1/2)) - LegendreP(n,2/7*14^(1/2))*4^n*14^(1/2*n))/n for n > 0. - Mark van Hoeij, Apr 23 2010
Recurrence: (n+1)*a(n) = 224*(2-n)*a(n-2) + 16*(2*n-1)*a(n-1). - Fung Lam, Mar 04 2014
a(n) ~ sqrt(1+2*sqrt(2)) * (16+4*sqrt(2))^n / (4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 04 2014
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-32*x*(1-7*x)])/(16*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 04 2014 *)
PROG
(PARI) a(n) = if(n, (4^(n-1)*14^(1/2*n+1/2)*pollegendre(n+1, 2/7*14^(1/2)) - pollegendre(n, 2/7*14^(1/2))*4^n*14^(n/2))\/n, 1) \\ Charles R Greathouse IV, Mar 19 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 04 2002
STATUS
approved