A135863 G.f. A(x) = 1 + 4*x*A(x)^(1/2); A(x) = 1 + 8*x^2 + 4*x*sqrt(1 + 4*x^2).

1, 4, 8, 8, 0, -8, 0, 16, 0, -40, 0, 112, 0, -336, 0, 1056, 0, -3432, 0, 11440, 0, -38896, 0, 134368, 0, -470288, 0, 1664096, 0, -5943200, 0, 21395520, 0, -77558760, 0, 282861360, 0, -1037158320, 0, 3821109600, 0, -14138105520, 0, 52512963360, 0, -195730136160

Offset

0,2

Links

Table of n, a(n) for n=0..45.

Formula

a(n) = -4^n*binomial(n/2,n)/(n/2 - 1), except a(2) = 8, for n>=0.

G.f.: (exp(asinh(2*x)))^2. - Philippe Deléham, Feb 01 2012

D-finite with recurrence: (-n+1)*a(n) +(-n+2)*a(n-1) +4*(-n+4)*a(n-2) +4*(-n+5)*a(n-3)=0. - R. J. Mathar, Jan 23 2020

From Alexander Burstein, Mar 27 2022: (Start)

G.f. satisfies: A(-x) = 1/A(x).

a(2*n+3) = (-1)^n*8*A000108(n) for n>=0. (End)

Prog

(PARI) a(n)=4^n*if(n==2, 1/2, binomial(n/2, n)/(1-n/2))

Crossrefs

Cf. A135864, A214377, A000108.

Sequence in context: A196282 A196332 A245654 * A176221 A021676 A122153

Adjacent sequences: A135860 A135861 A135862 * A135864 A135865 A135866

Keyword

sign

Author

Paul D. Hanna, Dec 02 2007

Status

approved